For me at least, a couple of lounge passes annually might make me choose to fly BA more. I'm *S with Turkish and Silver with Etihad (economy warrior), both of which are comparable to BA Bronze in my opinion, and for which I get a basic lounge in AUH and the one in IST. Turkish also grant lounge access if I fly domestic Turkish - so basically, for the same tiers on other airlines, I am getting lounge access at their primary base of operations only. I've utilised these about once a year.
Having graced GF and Galleries in LHR once or twice, they were both jam packed and I can see why you wouldn't want to open the floodgates to even more people. Nonetheless, the fact that BA Bronze gives me naff all that I care about (I couldn't care less about business check-in or priority boarding - it doesn't get me to my destination quicker) does mean I prioritise other airlines with my spend over BA - there is no incentive to fly more with BA as a Bronze unless I'm likely to make Silver, and as I don't fly premium cabins much, that isn't likely to happen. Equally, I probably don't contribute much to BA's margins so I suspect there is no love lost on either side.