All three of the things you mention are pretty easy to overcome.
I think you're missing the etc. in my statement. I simply gave a few examples of concerns. There are no shortage of challenges.
Weigh-ins: If you can't see a digital scale from 6' away, perhaps you might be missing important things on the mat, too. Time to hang up the shoes.
In high school, both teams must be present at the weigh-ins. Most of the time, the room where the weigh-ins take place is pretty small, the scale is set up in a location where the ref, and coaches from both team are too close. Often, at the beginning of weigh-ins, I move both teams back, but after 4 or 5 weights, it looks as though that never took place as both teams are crowding forward. Per current regulations, wrestlers could not be wearing a mask at weigh ins. The PIAA does have the ability to change that.
Neutral restarts: What is the magic in putting your hand between the wrestlers to restart? Stand back 6' and blow the whistle.
That's an interesting suggestion. I don't believe the NFHS rules specify that a ref must be in the traditional position (i.e., between the wrestlers) at the start. However, in the NFHS illustrations that accompany the rules, it specifically states "In the neutral start the referee should be in tight which will help to eliminate false starts and then back out." in that context, either the NFHS or the PIAA would need to change the rule, or give a special waver on the rule.
Raising the hand: According to one NCAA Division 2 college president, wrestlers won't be allowed to shake hands after the match, because covid, so the ref can just stand back six feet and tell the winning wrestler to raise his own hands.
Rule 6-5-2 from the NFHS rule book (end-of-match procedure): The wrestlers shall shake hands and the referee shall declare the winner by raising the winning wrestler's hand.
What the NCAA does is immaterial in this discussion.
A big issue is also wearing masks. There is no good way to wear a mask and also blow a whistle. And between raising hands, and starting from neutral, you're asking a ref to frequently put their hand to their mouth, when that hand may have been exposed to SARS-CoV-2 droplets.
In many fall sports, refs are trying out electronic whistles. The early word is that they are OK, but they can be difficult/impossible to hear in a loud environment.
Etc., etc., etc. There are a lot of obstacles to overcome for ensuring the safety of the refs in this environment. And even if the sport attempts to address many of them, it still comes down to how safe a ref feels. As I indicated earlier, the wrestling refs I've spoken with have a lot of concern at this time about reffing wrestling.