See this is where I disagree.
The only reason I do, is because you can tell if someone is an alcoholic, or on the path to alcoholism, their appearance begins to change.
Gambling addiction, especially since the emergence of apps, is so easily hidden. Would you know if a person sat next to you in the pub/train/match had just spent £5k on a bet, if they hadn't told you? But would you be able to notice an alcoholic sat next to you? Probably, because there would be a few things you'd notice.
I think bookmakers have introduced the limits purely as a buffer between themselves and a lawsuit. It's a perfect way to deflect blame and make it about the customer. This is why it should be a mandatory fixed limit over a period of time (day, week, month or year), in my opinion, because it still allows people to do the things they enjoy as you said, but within reason.
There must be thousands of unnoticed gambling addicts in this country, but how would you ever know?