Dropping 'to'

Continuing on with our critique of this quarter's "Grammatically Speaking", the second query says, in part,

"One way that I focused on was the use of to alone without its verb and accompanying clause in a sentence like He can leave work early today if he has to..."

But as they so often do, a student came up with a counter example.

"They don't need to be here precisely at nine o'clock. They can come a little later if they like."

Firsten basically throws up his hands. "It's because of that old problem we have in English concerning exceptions to some rules." We'll ignore the special status he implies for English, but generally this is not a very helpful answer. It is true that there is quite a bit of variability here, and that things are messy, but I think we can explain a bit more.

To be fair, Firsten does note that, where some verbs such as want, wish, choose, and prefer accept both the to and non-to complements, like rejects to. He doesn't, however, explain this: it seems to me that if you like is idiomatic such that without if, but still in the sense of would rather do something, we need would. Compare:

• They like to come late. -> They can come whenever they like to.
  
• They would like to come late. -> They can come whenever they (would) like.
  

There are other interesting things to note here, however:

• The phenomenon is most common where the to infinitive is functioning as a complement rather than, say, as a subject. Compare: Can we ask for a postponement?
  Yeah, I plan to. vs
  *To (ask for a postponement) would be awkward.
  
• It's not just after verbs such as want etc. that this happens. It's also common with adjectives that take to infinitive complements:
  I don't think I'll be able (to).
  
• Where the elided VP is headed by be or auxiliary have, we usually include them:
  the print quality is not what it used to be (cf. it doesn't look like it used to)