What's to answer? If your cloth is stretched correctly it's not going to do enough harm to even consider.
Many pool halls, thousands of home table owners vacuum their cloth. I've always heard the "old wives tales" about how vacuuming is bad but I've seen pool halls that used hand held dirt devils with beater bars after every customer, electrolux vacuums, "roombas," shop vacs, etc. Never have I ever seen evidence of it hurting the cloth. If it was gonna happen it would have by now. I challenge you to find one post of damage from a vacuum online. Does it wear some? Sure, but having a clean table is worth a possibility you might get a few months less out of cloth. Nobody wants to look like they gave Papa Smurf a handy j. Nobody wants their clothes filthy from playing. Nobody wants filth all over the balls etc. Not vacuuming isn't really an option.
Getting chalk dust into the air is a
legit health hazard. How many dust clouds have you seen due to brushing the table? I'd guess there may have been some old rack boys/men that had a hard time breathing later in life. Smoking was common, so who could say but it's possible.
On an un-vacuumed table, does the chalk underneath wear the cloth out faster? We know chalk has silica in it and creates friction.
How precise do you need to get to understand a vacuum ain't gonna harm a pool table? I mean, scientifically sure it will, but in the real world playing on a clean cloth is worth the minute wear, and it might increase cloth life since there's not chalk underneath rubbing the cloth from the bottom. It could be a neat experiment but the variables would be difficult to control.