Much research has been done on the extent to which home field advantage exists (it does, in some cases by a lot), and also why - Scorecasting determined referees are the primary driver, subconsciously tilting calls in favor of the home team.
The main hypothesis there though is that its the subconscious effect of rabid fans that influence the refs' calls - and this effect will presumably disappear with games coming back at neutral sites, without fans.
But how much will this matter? It's been a known effect in the NBA that improved travel and other technological perks have caused home court to decline in recent years - so will teams that have earned home court all season long (like the Lakers and Bucks) really be losing as much as they used to with no fans attending games?
NBA and NHL have seen declining HFA in recent seasons, with NBA having a very pronounced effect. Home court/home ice still exists, but to a lesser magnitude than it used to.
NFL and MLB have seen an even sharper decline, with each most recent season actually dipping to right at/below 0 - meaning home field advantage didn't exist last season.
Which leaves one domestic US-based league that has been bucking this trend, and actually is higher than its counterparts in other countries: