The phrase ‘Thinking of U and I’ is not ungrammatical because of the use of I. It maybe ungrammatical because of the use of U, although this is rather common today also.
I would like to say that I would never write like this as it would cause me too much distress.
It is important to note that what one means by ‘grammatical’ differs. The CGEL is a descriptive grammar and thus, when it says something is grammatical, it means well represented in the language.
In the following, % means grammatical in some dialects only and ! means non-standard.
The Cambridge Grammar of the English Language says this:
Because these coordinate nominatives are perceived to be associated with avoidance of stigmatised accusatives in subject coordinations they are often described as hypercorrections. This is to imply that they are ‘incorrect’, not established forms in the standard language. Construction [%The present was supposed to represent Helen and I, that was the problem] with I as final coordinate is, however, so common in speech and used by so broad a range of speakers that it has to be recognised as a variety of Standard English, and we will reserve the term hypercorrection for examples like [%They’ve awarded he and his brother certificates of merit].
Here’s the context of that paragraph:
For one variety of English, coordination has no bearing on case: the case of a coordinate pronoun is the same as that of a pronoun that could substitute for the whole coordination. Some examples conforming to this rule are as follows:
- At 4 pm this afternoon my ministers and I formally took office.
- He and Luckman were sentenced to life imprisonment.
- He and I have some of our biggest arguments over Conservative social issues.
- You know you can trust Andrea and me.
- I saw them and their children in the park.
- There has always been pretty intense rivalry between him and me.
Compare [1–3] with the non-coordinate nominatives I took office, They were sentenced …, We have …, and [4–6] with the accusatives … you can trust us, I saw them, … between us. This is the pattern advocated by the usage manuals, but for many speakers the case-assignment rules are sensitive to the syntactic distinction between coordinate and non-coordinate pronouns.
Coordinate nominatives corresponding to non-coordinate accusatives
- a) %The present was supposed to represent Helen and I, that was the problem.
b) %Any postgrad who has any concerns about working conditions or security in shared offices is welcome to approach either Ann Brown or I with them.
c) %It would be an opportunity for you and I to spend some time together.
d) %He had intended to leave at dawn, without you or I knowing anything about it.
- a) %They’ve awarded he and his brother certificates of merit.
b) %There’s a tendency for he and I to clash.
Single pronouns replacing the coordinations would have to be in accusative case: us in  and [2b], them in [2a]. One particularly common use of this construction is in the expression between you and I, and indeed usage manuals often discuss it under that heading. It must be emphasised, however, that these nominatives are found quite generally in coordinations functioning in positions where single accusative pronouns are used. The pattern shown in , with the nominative as final coordinate, is much more common than the one in , where the nominative occurs at first (or both first and final) coordinate.
There can be little doubt that the quite common use of this construction is related to the stigmatism attaching to accusatives in subject coordinations like those in [the first set of examples]: people are taught that Me and Kim will do it and Kim and me will do it are incorrect, and many generalise their avoidance of such coordinate accusatives to other functional positions. The schoolteacher’s strictures focus primarily on the 1st person singular pronoun (since this is where children most commonly depart from the standard variety), and in [the second set of examples], with final-only nominative, I is overwhelmingly the most frequent form that is found.
Because these coordinate nominatives are perceived to be associated with avoidance of stigmatised accusatives in subject coordinations they are often described as hypercorrections. This is to imply that they are ‘incorrect’, not established forms in the standard language. Construction [1 above] with I as final coordinate is, however, so common in speech and used by so broad a range of speakers that it has to be recognised as a variety of Standard English, and we will reserve the term hypercorrection for examples like [2 above].