Live audience is a great factor to boost up the confidence and hype of the players residing on that court but there might be times playing alone can still feel better because if you deduct the existence of live audience, the pressure on the players that they must win because it is their home court and all their supporters are there would be lessen.
Home court advantage would still be an advantage because players are more familiarize into their own court since the drills and practice games are being held on their own territory so when live game comes on, they are already familiar and can move freely around the court. It is just a matter of support when live audience are there but the advantage of playing on your own court will give the best confidence for the player on the court.
In a new normal approach there are countries that put manikins in substitution of live audience to let the players feel they are still having a support so existence of live audience won't be a problem anymore. It will still be relying on the team players on how they will perform during the game using their home court advantage even without the presence of live audience.
Well, the home court not only gives audience familiarity but rather the atmosphere. It's kind of a vague thing, but hell, players understand it well enough I suppose. It's basically the fear of going to somewhere unknown for others, while being at home for someone else. We're all afraid of the unknown, and players going to foreign courts to play could prove that they are pressured as such, whether there is an audience or not.
its still some advantgae
two more factors
1 is travel sucks and traveling too a new city to play always affects players even more usa because its so big
2 hoe players can rest and dont really care about being in same city as awlays they can relax and play more normal
Ask any professional player out there. If they think traveling sucks, they should probably quit already tbh. It's not a matter of it being big, players would only hate traveling if they were pushed against a stupid schedule, but if things were planned properly, traveling can even be a form of relaxation. Players are also given the time to adjust their mindset afaik. They give them some time to roam the city to adjust the "unknown city" mindset, making their mentality the same as being in the home court, or at least, making it as close as possible to that type of mindset.