Nikola Tesla was a great engineer and innovator—and showman—who's been mythologized beyond all reason.
Even at the time, Tesla's greatest contributions were being simultaneously discovered by contemporaries like Galileo Ferraris. Discovery marches on, and is more a product of the existing body of scientific knowledge than of any one man.
There have been too many other great minds in physics and electrical engineering for it to be remotely plausible that we've missed out on "countless inventions" that would be available to us today, if only Tesla had more money for his experiments.
Even at the time, Tesla's greatest contributions were being simultaneously discovered by contemporaries like Galileo Ferraris. Discovery marches on, and is more a product of the existing body of scientific knowledge than of any one man.
There have been too many other great minds in physics and electrical engineering for it to be remotely plausible that we've missed out on "countless inventions" that would be available to us today, if only Tesla had more money for his experiments.