To work it out,

7x65r max pressure is 50,000 psi. Area of head is .224 sq in, hence thrust is 11,200 lb

Compare to the 16 bore shotgun

Pressure is 11,500 psi. Area of head is .78 sq in hence thrust is 9,000 lb

So yes the rifle gives a bit more theoretical thrust, but not that much more than a 16

Now most shotguns survive tens of thousands of rounds before shooting loose. Most rifles probably only shoot a few hundred rounds in the course of most lifetimes. My 7x65r shoots half a dozen animals a year and probably a further ten to 20 rounds zeroing / practice. You can easily shot a couple of hundred cartridges in one session at the clays. That's five to ten years worth of 7x65r shooting.

Given that most 7x65r are built on strong actions with cross bolts etc you are far more likely to wear barrel out than shoot it loose.