Not sure we can compare a beaver to a Lynx. Beavers are knot known for claws and canine teeth
But I know what you mean.
I think the issue over the terrain not being suitable for a dart will be around the risk to the shooter if the dart does not make good contact. The rifles used are quite low powered and accuracy is not great. The last thing they need is a Lynx that's been half sedated and that has a dart hanging out its backside.
Anywhere where the shot is not completely clear and where "muscle" cannot be hit, then I am afraid its the old proper rifle if a risk to the population is deemed possible.
I can imagine a Lynx getting a bit upset if pursued.
And back to beavers. We were down in Tayside/Perthshire 2 weekends ago. I took cass to a bit of river I used to fish about 10 years ago for Pike. From being a treelines deep stretch, it is now almost devoid of trees, and the bank has collapsed in some parts, causing a shallow, fast running section rather than the deeper, fish holding areas that were there before. Used to produce big grayling too.
All what was left was knawed stumps.