The thing is, "piano first" covers a lot of different ways to open a concerto. Depending on how it is done, a piano flourish between an orchestral introduction and a traditional ritornello can be an effective opening to a concerto - as though the piano decides to make its presence felt, then allow the orchestra to whet the listener's appetite for more piano. Examples of this include Beethoven's Concerti No.4 (minus the orchestral introduction) and No.5, the aforementioned Brahms No.2 (one of my personal favourites, and in addition to being the closest the piano gets to a cadenza in that movement, the piano passage at the beginning introduces thematic ideas which return later in the orchestra), the Liszt No.1, and many others. Then there are concerti which open with a piano flourish, then introduce only one or two themes in the orchestra before the piano takes them up - the obvious examples here would be the Schumann and the Grieg. With the Tchaikovsky No.1, the piano is almost another instrument of the orchestra during the introduction, but one without which said introduction would not be nearly as effective. (Although I know cynics who think the entire piece is ineffective. I don't share this opinion myself!) After the opening chords of the Rachmaninov No.2, the role of the piano is rather similar to that in the Tchaikovsky (incidentally, if memory serves, those opening chords return in the early moments of the finale). Something similar yet not identical happens in Mozart's 'Jeunehomme' concerto, K.271, where the orchestra and soloist establish the primary theme with a sort of dialogue (then the earliest entrance of the piano in a piano concerto if I'm not much mistaken). And then there are piano concerti where, if the piano is not the first instrument one hears, it is the first to establish important thematic material which might not be nearly as effective as it would be were it played first by the orchestra. The Rachmaninov No.3 is perhaps the most famous example of this, but there's also the Bartok No.3 and the Shostakovich No.2.
The point is that while I don't know that I prefer concerti where the orchestra does not have the traditional Baroque/early Classical opening ritornello, the openings of such concerti can be very effective if done well, and it's hard to imagine them done any other way. In the end, I suppose the more effective instrument to use in setting the stage, so to speak, depends on the scene the composer wishes to present. For example, I can't imagine the lyrical opening to the Prokofiev No.3 sounding nearly as effective played on the piano (for a start, I've tried reducing it for piano and while I'm not the best reducer of orchestral pieces it still sounds flat and lifeless even allowing for my lack of skill), and removing it altogether would kill so much that is good about that movement. Meanwhile, in the Chopin concerti, those opening ritornelli are among the few moments the orchestra is playing anything interesting, so I say let them have their fun.
