What did you used to do?

Page 496 of Collins Cobuild English Usage reads

You form 'yes/no'-questions with used to by putting did in front of the subject, followed by use to: Did you use to do that, when you were a kid?

WARNING: many people use used to instead of use to in questions. However, some people consider that this use is incorrect,

Did you used to play with your trains?

If the 'wh'-word is the object of the clause, or part of the object, you use the auxiliary do after it, followed by the subject and used to,

What did you used to do on Sundays?

I'd like to know why use to isn't possible in the second structure, What did you use to do on Sundays?

USED: https://oed.com/oed2/00273881

The normal, completely unremarkable negative (with Do-Support) of the idiom used to in

• I used to like marshmallows.
  /a'yustuˌlayk'marʃˌmɛloz/

is pronounced (note the /st/ in both forms -- no /zd/ for used in this idiom)

• /aydɪdṇ'yustuˌlayk'marʃˌmɛloz/

and that's not a problem. In speech.

There isn't even much confusion with the almost identical idiom be used to, meaning 'be accustomed to' -- most English speakers don't even notice that there are two of them.

But the past-tense-with-presupposition idiom used to does pose a problem, in writing. In speech it's treated as an infinitive, as required by Do-Support, no problem. But in writing used doesn't look like an infinitive; in fact, it's a past participle. But the idiom is spelled used to. Hence, there are two choices:

a) I didn't used to like marshmallows.

b) I didn't use to like marshmallows.

Both of these look wrong to experienced English readers, because both of them contain sequences readers have been taught to avoid as products of grammatical mistakes:

• (a) contains didn't used, which is wrong -- Do-Support doesn't make a participle used.
  So that looks wrong.

• (b) contains use to instead of used to, which is the idiom, so use gets a /z/ .
  And that looks wrong, too.

Too bad, so sad, English orthography flunks again.