I've used cradle straps for at least 40 years and have never had to detach the strap to put it in a regular case. The trick is in how you wrap the strap around the banjo pot, it will fold on itself and sit comfortably on the flange. It's different for different case types, the current case I have for my Nechville is the tightest fit yet but the strap still rests comfortably in the case attached to the banjo without being crushed or creased in any way. Without doing that yeah, for sure, the strap can get damaged.

In all these years I've only had two cradle straps and they never got damaged and performed just find for decades each. The strap on my banjo now has been in continuous use since about 2002 on two different banjos. in two or three different cases. It's come off only when I had to do work on the banjo.

If interested I'll take a pic or two and post to this thread, if it helps.

I have never had a problem with my cradle strap. It fits snugly but easily in my banjo case. Maybe, as Frank said, it's the way you attach it to your banjo.

I've had 2 cradle straps in the 30 plus years I've been pickin' and the only reason I got the 2nd one was because the sheep skin on the first one got to the point where it was packed down to hard it didn't cushion my shoulder.

Original poster said full width. If strap is over two inches wide I think I would have a problem.

I bought a new cradle from Stewmac for a customer who changed their mind, so I now use it.
It's thicker not wider, more stiff as new.
Otherwise it fits.
Different shoulders or old injuries require personal fit.

Thanks for the responses, which I find surprising, because none of my cases (Stelling, Gibson and Deering) are wide enough to accommodate the strap wrapped around the resonator, or deep enough for it to sit on the flange without impeding lid closure. And yes, I’m taking about 2.5 inch wide straps.

Depends also on the strap. The Lakota Leathers I have on all my banjos are so soft they just fold right into the case (adding extra protection I might add).

I find straps 1 3/4" wide are comfortable and still fit in the case between the flange and the lid.

To clarify my first post, it's not so much how it's attached to the banjo I was talking about, but how you fold it on itself in the case. In other cases I've had there was open space at the heel in the case so I could push the thin cradle part of the strap into that area then wrap the strap itself around the pot in a certain way that I stick with once it's figured out. In the current case there is no space behind the heel so I had to come up with a new way to layer the strap back in and on itself as it flows around the pot.

My old Long Hollow Leather cradle strap is stiff leather and 2" wide and fits fine. Not sure if the extra .5" width would change that or not. It might.

The banjos you mention, Stelling, Gibson and Deering all make similar 11" rims with 14" resonators, not the 13" imports.
So they have taken a path to make their banjos fit snugly rather than have any slop during shipping and transport to the gig and back home. We know many banjos suffer breakage each year. Ouch.  Also all shipped banjos get charged extra because they are sized over the allowed limits
I have two hardshell Gold Tone longneck banjo cases, one for openback and one for resonated. GT no longer offers a bluegrass flathead longneck, so TKL no longer builds that. But that is irrelevant. I have no trouble fitting a cradle strap into either case.

Acoustic Music Odium needed a serious and simple case rack, and we plan carefully. We looked at many different type of hardshell and soft cases and we found: 6" seems to be the standard, no fives or sevens.  Calton has different specs, but everything fits our case rack!

I have also heard an urban myth that storing leather on or on top of guitar strings and finishes causes problems with your finger oils and spare dead skin cells interacting with the tannin in the leather which is acid, not alkalai.

Steve Davis is a member here and is very familiar with nauitcality and uses sturdy rigging clips to unhook his cradle shoulder strap and use it on various banjos.  

I have Hemp harnesses for my dogs' comfort.  I have wide hemp strap on my '58 Epiphone Texan.  Everything goes into the cases nicely.

Thanks, all. I guess my problem is that I have recently replaced an old leather type cradle strap, that was starting to split where it was folded back on itself around the flange, and fray where the top edge was crushed by the lid, with a new and fairly expensive leather strap of similar width (2.5 inches). The leather on the new strap is quite stiff and does not really like being folded back on itself, and I’m not keen to shorten its life in the same way as the old one, but detaching and re-attaching every time is just not practicable. The question might be then, why do they make these wide straps, and why do we buy them?

I did go to one gig with a banjo in a soft shoulder case, but it wasn’t a good idea. Somehow, the fifth string peg got knocked out of its socket whilst it transit, and it took quite a while to reinstall it, just when we should have been sorting sound levels, etc. File under not to be repeated!

"fray where the top edge was crushed by the lid, with a new and fairly expensive leather strap of similar width (2.5 inches)"

I see the difficulty for the poster.  The typical distance from the top of the flange to the top of the tension hoop is around 1-3/4" - 1-7/8".  Since the strap is 2.5", laying it sideways on top of the flange will result in the strap sticking up above the tension hoop about 5/8" - 3/4".

If it's a good fitting case where the cushioning contacts the top of the tension hoop to keep the banjo from moving, then the cushioning is crushing the edge of the strap, and more force is needed to close the case.

So something has to change (assuming the banjo and case stay the same) -- the case padding, the width of the strap, the type of strap attachments, or the method of storage.  I don't have a solution.  My straps are 1-1/2" wide and all is well in the shire.  

The poster wants to keep the 2.5" width of the strap and the cradle-type attachment.  Without the cradle design it would be simple to put some plastic clips on the ends of the strap to make it easy to attach to, and detach from, the hooks, and store the strap in a different way, same as one would do with a guitar.

the last strap i had made was 3 inches ,,well that didn't work to well so i had the guy cut it back to 2 1/2 inches...it works but there is some pressure on the flange in the case,,, but now its got so old its loosened up a bit and ain't too tight in there,,, but the extra does secure your banjo good and snug........

I filled in with a group for a while, playing a square dance session many years ago where we might play the same song for 15-20 minutes. My bony shoulder required me to get a wider strap. I found one made of fairly stiff leather about 4" wide that helped me survive a few months. It was thin enough to slide down the side of the resonator and fit well. I stayed with 2 1/2" width and have always found a way to wrap around outside the hooks in some fashion. A new stiff strap would not be likely to conform as mine do. I have never resorted to laying across the strings.

Thanks Alex for summing up my plight so well. And yes, there seems to be no easy answer, other than a change of strap or wait until it softens up through constant crushing and becomes as unsightly as its predecessor. Then there is the extra pressure on the case clasps and fixings by forcing it shut, or do I just need to get out a bit more?

New strap.  Golden Gate, Huber, Lakota etc.  For $20-80 for a new leather strap 1-1/2" wide or so, the difficulty disappears.  Done.   No worries, no damage, no posting on the BHO, no trouble at gigs, no mental anguish, etc. 

The recent strap you already bought is irrelevant, like money already put in the pot in a poker game.  Think of the cost of that strap as tuition in the school of experience.  

https://huberbanjos.com/shop/huber-leather-banjo-strap/

https://www.elderly.com/pages/search-results?q=banjo%20strap