Lets break this down to specific questions:
after each of the early shuttle launches, 100 or so thermal control
tiles were found missing. These had to be replaced before each
subsequent flight. Why [were] the lost tiles were there in the first
place if they apparently weren't necessary for thermal protection in
the area of the shuttle where they were placed.
There are several assumptions here, which are not supported in fact. There were many spots of tile damage greater than 1 inch (25mm) in diameter. That's not the same as a missing tile, and the design of the tiles may have included increased thickness to allow for expected abrasions, dents, etc.
I would be surprised if there were hundreds of missing tiles. Hundreds of spots of damage greater than 1 inch in diameter is quite a different thing. Each tile was several inches thick and its likely they could meet specification even with some amount of damage on the exposed side.
There are multiple books about the detailed design of the shuttle and the operating regimes they were expected to face, and actually faced. Perhaps the first step is identifying kinds of tile damage (<1% of depth affected, >1 inch skin face affected <10% of depth affected, tile missing, tile and adjacent tile missing.) you care about, or that someone has already studies. Then you need to get the title damage survey data. Chart damage kind or instance by launch date.
Columbia, the Shuttle lost from surface damage, was not destroyed by tile damage. It had its carbon-carbon leading edge damaged. Different material, common damage mechanism (foam falling off the booster tank).
was just dumb luck that more shuttles weren't lost during re-entry?
A very large question, but almost certainly luck, aka capable design, competent manufacturing, responsive operators, redundant systems, conservative rules, occasional reasonable management, played a role.
Was it just luck that these tiles just happened to come off in areas
where their thermal control was not necessary?
Objection. Presumes hundreds of tiles damaged == hundreds missing. Missing is different and far more dangerous. If you can get tile damage and tile missing data, a composite plot of the locations which lost tiles, which suffered damage > 1 inch diameter, > 1% of tile thickness, > 10% tile thickness, and lost tiles AND adjacent tiles would be worthy reductions of fact, on the way to information.
Perhaps they came off after the major portion of the re-entry was
completed and the thermal loads were not very high?
Earlier response indicates majority lost during ascent, which makes sense because: Fast in dense air, tank shedding insulation not present on re-entry,
water, ice, bird exhaust, etc, more likely from Earth rather than orbit.
Was the fly-off of these tiles a potential source of vehicle impact
damage during re-entry?
Another respondant says, "No"
this problem seemed to go away, how were fixes made?
meaning tiles, not including leading edges? As noted, big efforts to keep foam from shedding from booster.
Anyone have any detailed knowledge (damage reports, analysis reports)
of the impact these lost tiles could have had to the vehicle?
You might adjust this question once you know more of what actually happened.