There has always been 'home advantage'; whether fast and bouncy in Australia and the Caribbean, slow and turning in Asia, or swing and seam in England and NZ. Teams and players have adjusted to the conditions.
The noticeable difference today, however, IMO, is that there are different formats of the game, which each require their own techniques and strategies. T/20 players (generally) will lack the technique and application to play a five day Test match. Likewise a player like Pujara (or a Boycott) wouldn't be able to play the shorter game to the required level.
How to make Tests fairer and more equal? No easy answer, but away teams do win Test series fairly often, so I personally don't think a change is necessary.
I'm a traditional old fart who doesn't like change.