Hypermobility is not THE problem. And resolving aching shoulders is not just about bending the elbows...
Aching shoulders can come from a number of areas. But your mention of 'hypermobile elbows leads me to deduce (for lack of further info)
That you ARE 'straigtharming' (in your hypermobile way...) and locking the elbows. Along with that comes a bunch of other contributing factors, like hunched shoulderrs.
You're not unique. Many riders I see on road bikes and hybrids (which actually cause/exacerbate this issue) have this issue to some degree.
My earlier post/link covers much of how to resolve these poor posture issues - not all.
That they ride the way they do, is totally up to them. Not my crusade. But I lucked out and had some good tutelage when I first became more involved in riding.
Ultimately the issues fall to a lack of using some core muscle and back strength to help in holding up the torso. Either due to poor strength or just poor understanding.
Once there is realization, there can also be adaptation, in a more personal way, for each rider. Of course, some just chose to continue on as is.
Ride On