On the one hand, a sign like this definitely did have enough room for the full spelling of “through”. There seems to be no reason to abbreviate it.

On the other hand, isn’t drive-thru just, like, its own noun now? Part of me thinks this was always spelled correctly.

It seems like shorthand for signs that has been used enough that it’s basically normal now, like “lite” instead light, or “donut” instead of doughnut.

“lite” has a different meaning (or at least connotation) to “light”