Chainsaw Protective gloves are one of the most useless, ill thought out products on the market. To answer your question, no I don't think we need them in the modern environment. Reasons:
1. Chain catcher and rear hand guard provide protection for the right hand.
2. No protection in the right hand in most chainsaw protective gloves, so a normal (better fitting) pair of gloves provide the same protection.
3. Inertia chain brake and chain brake with integrated hand guard on modern saws provide protection to the left hand in the event of a kick back. Chain does not come back and hit left hand if it snaps/comes off (unless you've got a saw that works in reverse!)
4. Protection rating (only on the left hand, remember) is inadequate in any glove I've seen on the market for current chain speeds. Left hand normally rated only to 16m/s and right hand is, yes, not protected at all (beyond what a normal glove would offer)!
5. They are crap in the wet, increasing the risk of your hands becoming cold - white finger and loss of control of the saw.
I am prepared to accept that we should wear gloves for saw work to protect our hands from cuts and scratches and to keep them warm to reduce the risk of white finger, but these should be well fitting and easy to work in - two things it is very difficult to achieve in a chainsaw protective glove. Several pairs a day may be appropriate if working in wet conditions.
HSE and FISA both acknowledge that "suitable for task" gloves should be used, not necessarily chainsaw protective gloves.
Unfortunately for you, if your employer says you need to use a piece of PPE then you need to use it. They make the rules for their employees when it comes to this sort of thing. What you can do is try to convince them otherwise, point number 5 in my list is probably the most worthwhile argument as there is a very genuine increased risk to H&S in this case by using the prescribed PPE.
All in all, it is very tiresome having to constantly risk assess chainsaw gloves out. It would be much easier if everyone would just accept that they are useless and move on to requiring a pair of well fitting protective gloves.