You've raised a really interesting point - but one which I basically disagree with.
First off, I'd rather have players that excel at cricket than players that are great drinkers. Yes the Ian Botham of c1988 would have a lot of stories and drink a lot of beers but should not be mourned as a player.
The complaint "where have all the characters gone" is a constant refrain in every sport in every era. And because of that, we can be pretty sure that it's likely to be false. The myth is reinforced, for understandable reasons, by a great number of ex-players-turned-pundits. I'm sure that there are plenty of characters now, we just don't have the perspective to see it (and perhaps they play the media game a bit more cannily than they used to). Freddie, Ponting, Lee, Collingwood, Swann, Sidebottom, Broad, Hauritz, Clark all seem like reasonably interesting characters to me. Given time we'll forget the boring bits and remember the more interesting bits - that's human nature.
There's a real risk of rose-tinted vision here. To take 3 of your English examples: Botham, Gower, Gatting, they were all wonderful players in their different ways, but none of them was someone I'd particularly want to spend any time with. Botham talked a good beer, repeatedly, but there's a risk of mistaking that for being a good bloke rather than a bully and a pillock; Gower has proved himself since his retirement to be the antithesis of charismatic; and the fact that Gatting ate a lot and shagged a barmaid doesn't add up to being a character. There were plenty of fools and unpleasant characters in those days; and plenty of utter non-entities too, whom we of course forget.