DmitryFarber
Vatsal7794This is a very normal construction. When we use the relative pronouns "that" or "those" in a comparison, they refer to the previous noun without the previous modifier. So if I say "Apartments in New York cost more than those in Burlington," "those" refers just to apartments, and we are free to apply the new modifier. If I say "Apartments in New York cost more than they do in Burlington," then I have a problem. "They" doesn't work like "those," so this sentence would be saying that apts in NY cost more than apts in New York cost in Burlington. If that doesn't make sense to you, it's because . . . it doesn't make sense.

If for some reason we wanted/needed to keep "they," we could rewrite by applying our modifier to something other than "apartments": "Apartments cost more in New York than they do in Burlington."
Great examples, DmitryFarber!
To tease this out just a bit more, the distinction Dmitry is pointing out again comes down to parallelism.
In the broken example,
"Apartments in New York cost"
parallels (with "more than")
"they do"
Here, "do" acts as a bit like a verb-analogue of a pronoun, standing in for the verb "cost." And it becomes apparent that "they" has to refer to "apartments in New York," which creates the nonsensical description of what "apartments in New York cost in Burlington."
Contrast that with
"Apartments cost in New York"
parallels (with the split "more than")
"they do in Burlington"
And in this case we see that "do" again parallels and stands for the verb "cost," but now the only word before "cost" is "apartments," so "they" must stand for simply "apartments" and the remaining elements "in New York" and "in Burlington" also parallel nicely. The result is the logical description of what "apartments cost in Burlington."
Or try
"Apartments in New York cost"
parallels (again with "more than")
"those in Burlington [cost]"
The word "cost" is implied in the second half, thanks to parallelism. And yet again the parallelism makes clear that the pronoun (here, "those") stands correctly for "apartments" and nothing more. Again the logical result is a description of what "apartments in Burlington [cost]."