Current Starlink satellites are 800-970kg[1] and 100% of their mass is vaporized on reentry, so 1-2 satellites a day would be approximately 1.5 tons per day added to the atmosphere. The atmosphere's mass is 5.15 quadrillion tons. Even if satellite vapor stayed in the atmosphere forever, it would take approximately 10,000 years before it reached 1 part per billion.
This is correct from the perspective of direct health hazards, but there are still plausible risks. We know from history you don't need a lot of mass to cause global problems, if the material is catalytic.
If the vaporized satellites were entirely converted into a compound that was as damaging to the ozone layer as the most potent CFC (R-12 [1]), and the compound stayed in the atmosphere forever, it would take 5,000 years to reach current atmospheric concentrations of R-12.[2]
Vaporized satellites really don't seem like a concern.
The first is that IIUC, CFCs release chlorine atoms which catalyze ozone, whereas aluminium oxide catalyzes the creation of chlorine atoms from chlorine reservoirs, which then go on to catalyze ozone. I loosely believe at this point after some sketchy research and maths that this makes it around two orders of magnitude more potent.
The second is that these particles are produced directly in the upper atmosphere. I couldn't give you a number for how much that changes things, but I assume it's nontrivial.
The final point I've noticed is that mass to orbit has been increasing at a rapid exponential rate recently, and it would not surprise me at all to soon see an extra order of magnitude on it.
Worst-case, that could change your 5,000 year figure to just a couple. I don't think it's that bad, I'm not overly concerned about this issue, but given ozone depletion is a legitimate existential threat and the numbers don't immediately make it seem impossible, I think it's worth paying attention to.
My point is, Starlink is doing this now, but they are continuing to scale up. Other companies are going to follow. Is there a point that this does become something to worry about because the scale has increased?
The highest numbers I can find for the final Starlink constellation is 40,000 satellites. Let's assume Starlink and its competitors have constellations totaling 100,000 satellites, and satellites need to be replaced every five years, and each satellite weighs 1 ton. That means 20,000 tons of vaporized satellites per year. The atmospheric emissions would be 3.88 parts per billion per year. This would still be less than the mass of asteroids and space dust that burn up in the earth's atmosphere every year.
If the reentering satellites were somehow transformed entirely into chlorine gas that somehow stayed in the atmosphere forever, we would reach the OSHA permissible exposure limit of 1ppm after 250 years. Chlorine is detectable by smell at 3ppm, which would take 750 years.
It's very likely that the vast majority of the vaporized satellites are inert, as they are basically incinerated on reentry. It's also likely that most of of the vaporized satellite does not stay in the atmosphere for very long. The only way this could be a problem is if the satellites emit a long-lived compound that catalyzes a reaction in the atmosphere, similar to how CFCs destroy the ozone layer. So far, the only candidate for that is aluminum oxide particles, and solid rocket boosters create more of that than reentering satellites. (Fortunately aluminum oxide isn't nearly as bad for the ozone layer as CFCs, and SpaceX does not use solid boosters.)
Also once you are launching tens of thousands of tons to orbit per year, it starts to become feasible to build infrastructure in space. Satellites at the end of their service life contain valuable raw materials. It would likely become cheaper to refurbish or recycle them rather than deorbit and launch new ones.
So basically it's not worth worrying about.
1. https://en.wikipedia.org/wiki/Starlink#v2_(initial_deploymen...