Television, technology, and fan-pressure.
Last things first: almost every matchday in English soccer, there is some lower-tier club that tries to skimp on the grass; playing on a pitch that is divoted, dug-up, and dingy. And the fans – their own, and opposing fans, as well as looky-loos – will absolutely pummel that club with snide comments, jokes, and general shit-talk. Heck, this just happened in an Olympic soccer match and it led to some serious uproar. And that field endured (IIRC) nine matches in nine days.
The technology and money involved in baseball - at all levels - leads to much better groundskeeping than back in the day. It's just easier to cultivate and keep a lush field of grass these days.
But really, things improved because of TV. I'm old enough to remember all of the shitty astroturf fields of the 1970s and how GREEN they were painted. Natural grass fields wanted to compete with the fake-hues of astroturf during the network Game of the Week. Owners wanted their field to look better than the other guy's field.
We in Boston were late to this party, as John Harrington didn't give a shit about anything other than making money, so in addition to the sewage in the concourses, the field looked like shit regularly into the early 2000s. But the HWL group does care about looking good, and has put a lot of work into improving the field. It was not long ago that Fenway was an awful playing surface that resulted in shitty hops and uneven bounces. Getting rid of that was a necessary by-product of improving everything about the team, and fan, experience.
