There are better quality NEMA receptacles (at least in NEMA 14-50) which corral the stranded wire. These are recommended for heavy duty use such as an EV charging connection. One recommended brand is Bryant. I got a Bryant NEMA 14-50 to redo my kitchen range connection (50 A breaker), only to discover it is rated for copper only. I have stranded aluminum and cannot use it unless I pigtail the aluminum or get a copper ferrule which is rated for aluminum conductor. Then I would need the crimping tool to make the proper crimp connection.
Twenty years ago I installed the NEMA 14-50 rated for copper and aluminum that has been in place since then, seemingly without problems, but I have not examined it since.
When I installed it I had the same complaint you describe -- the screw splayed out the strands and it did not tighten as hard as I was used to for solid conductor. I did not use a torque screwdriver. I did coat the aluminum conductor in Burndy Penetrox before makng the connection.
At about the same time I redid the dryer receptacle (30 A breaker) also fitted with a cable with stranded aluminum conductors (smaller diameter than the 50 A range circuit). For the dryer receptacle connection I pigtailed the stranded aluminum conductor with solid #10 copper.* This tightened hard.
In your case you have stranded copper conductor so you could use the appropriate twist on connectors to pigtail this with solid copper 10 AWG. Of course, a clothes dryer does not use use high enough current for long enough to require highest quality in this connection. If you would just tighten the connection according to the instructions (explicit or implied) and put it into service it would almost certainly perform acceptably. However, I do have more confidence in my dryer connection having been pigtailed with solid conductor.
*I used grey Scotchloks twist on connectors filled (by me) with antioxidant compound (Burndy Penetrox) to make the aluminum to copper connection. In my experience this will make a properly performing connection, but Polaris connectors torqued to specification would be much higher assurance of a non heating connection.