Has the pronoun "me" been discarded from general usage? More and more, I hear people say something like, "He served pizza to my sister and I" or "Between you and I, that dinner was not very good." It seems the nominative is out of favor.
Has the pronoun "me" been discarded from general usage?
Quite the contrary. In ordinary colloquial English object-form me has largely usurped the function of subject-form I. I is almost never encountered as a predicate these days—"It is I" is insufferably pompous—and is increasingly rare in conjunct subjects: you are far more likely to hear "Joe and me went" than "Joe and I went".
The contrary use you hear is a hypercorrection. People with an imperfect grasp of the Standard English (whatever that is) have been badgered throughout their school years to avoid X and me in subject contexts, so in relatively formal discourse they strain to speak 'properly' by replacing me with I—as often as not in object contexts.
A construction such as to my sister and I is often rationalized as a hypercorrection, the application of a grammar rule in the wrong context, the assumption being that having been taught to avoid something like:
My sister and me went shopping.
some native speakers instead avoid it even where it belongs, as in your example sentence.
The actual state of affairs, however, is that any construction on the pattern
[personal noun] and I
is being felt more and more as a single noun phrase whose elements are fixed. Otherwise, it's difficult to explain why so many native speakers would come up with
This usage dates, at least in print, to around 2004, but can in no way be parsed as a hypercorrection. No new possessive personal pronoun *I's has been coined: it is merely the logical outcome of treating the x and I construction as a fixed unit that resists being declined for case — except, of course, this novel way of forming the possessive.
Pronoun paradigms like I, me, my/mine and a few strange plurals like child-children, along with so-called "irregular" verbs like sing, sang, sung and comparisons with -er and est, are some of the few grammatical remnants of English's Germanic past. It's no surprise, then, that with pronouns there is a tendency toward paradigm leveling, eliminating morphological distinctions such as case from everyday, unfiltered language and considerable insecurity in determining what is "correct."
You hear "between you and I" more and more these days because most people have no idea what is correct. You even hear professionals say, "Call the nurse and I." Or worse,"Call the doctor and myself," because people assume (Wrongly!) that me/myself/I are interchangeable. They are not. They have their own specific uses. The perfectly good pronoun "ME" has been so maligned by parents correcting little Billy from saying, "Me and Joey are going to play." So all Billy heard being drummed into his head was: Joey and I, Joey and I. So, no matter the circumstances, Billy did his best to never utter the word "me" again, even when used as an object. So, whether the subject or direct/indirect object of a sentence, the word "me" was wiped out of little Billy's vocabulary, making no distinction between its legitimate and accurate use.