As has been said there really is no chemical substitute for psychotherapy and positive habits like a good diet and exercise for managing anxiety.
That said, everyone has a different struggle in life and it's no doubt a harder road to getting anxiety under control via non-exogenous-chemical means for some than for others.
I don't have any personal experience using benzos to manage social anxiety, but I did use phenibut quite often until very recently (a few months ago in fact). However in my own experience this caused several problems even though I never developed a physical dependence. Firstly, while I was on it it made me too content with situations in my life that actually I was not happy with - and therefore prevented me from developing the motivation to actually take difficult actions rather than maintaining the status quo, which was quite tolerable while in a phenibut-induced state of artificial bliss.
Secondly, I started to feel that it was inhibiting my growth as a person after a certain point. I found phenibut useful up to a point, definitely, because it made me realise what I was capable of without these illusory barriers of anxiety and self-doubt, and what life could be like if I overcame them - and I would imagine benzos could be useful for the same purpose - but phenibut was a crutch, and I realised eventually that if I never or only rarely attempted to try to take difficult actions without this crutch, then I was never going to grow. I can't speak for anyone else of course but I found myself thinking things like "I must make sure I'm on phenibut for this", or "if only I was on phenibut right now!" during situations that I found psychologically challenging, and I think once you start having these thoughts then continued use of such "crutch substances" can be actually quite counterproductive, because you can start to talk yourself out of being brave, with the excuse that you're just not on your crutch substance of choice right now.
All that said - it's hard to say if this was a realisation that I could have had or should have had earlier, or if it's just taken as long as it did because that's how long I needed to develop the psychological resilience to abandon using such crutch substances. Everyone is different and as I said everyone has a different struggle, but I would just urge caution with using GABA-ergic susbtances for social anxiety except in the very short term, because even if you never develop a dependence or a problem I think there are more subtle negatives which are easy to overlook.