I have played music for most of my life and tried to learn everything that I either wanted to learn or felt that I needed to learn to progress. I have also never seen the point of having 30 minutes warm-up sessions before playing since that removes the convenience of being able to sit down at the piano and simply play at a moment's notice. I want to be able to get an idea of something that I wanna play or practice and just do it without warming up every time. If I need a warmup for something, I find that a little noodling does the trick. I feel that having a tight practice schedule with the same scales and chords would take all the fun out of playing. To be quite honest I never really felt like I was practicing since I only play what I think is fun and I find a sense of progress fun.
Because for most of us, playing music is a pleasure, we tend to play what gives us that pleasure. It's part of human nature. As is avoiding tedious stuff.
Warm-ups in music, I see as rather different from those in athletic sports. Yes, they're important for warming up certain muscle groups - although having warmed up glutus maxima never really made me play piano better... But also a warm-up is important mentally. Before sight-reading something, I encourage my students (and myself) to play scales and arpeggios in that particular key. 'Putting my E♭ hat on', so to speak.
So, instead of 'mindless' warm-ups, it's worthwhile using that time (and 30 mins is way too long) to 'get into the zone'.
Practice time itself is for a variety of purposes: learning new stuff; improving playing what's on the back burner; eliminating annoying recurring mistakes; practising some sight-reading; trying out new techniques are some examples.
A big influence will be what one does it all for. Self-satisfaction, working towards an exam, being ready for a band rehearsal, preparing for a concert performance are some, and the regime is different for each. I think we all have different goals, and different ways in which to attain them. What works for one may well not be successful for another. There are those who sit for ten minutes and are then bored - but can do that five times a day. There are those who can sit down for three hours and are still productive in the final five minutes. We all have to find our own best practice - literally - and that's something a lot of teachers don't discuss with students, sadly.
I used to have a similar view of warming up as you did. Back then, warming up felt like a waste of time to me. I remember immediately jumping onto a song I just want to learn instead of practicing scales or warm ups. However, now I see things differently. It is important that if you strive to have your skills developed professionally, you should involve yourself in various techniques or methods, regardless of it being fun or not. Professionals constantly learn to progress. In fact, the results of those constant practice might be worth it.
Otherwise, if you plan to play an instrument as part of a hobby, then there is no need to pressure yourself into having a fixated schedule. Passion is important and that's what drives us all into improving ourselves. I believe that it's best to sometimes nudge yourself time to time if you want to progress but don't overdo it to the point you loose your motivation. Everyone has their own ways of growing their skills, you don't have to follow them precisely. Music is supposed to be enjoyable, not a tiresome obligation.
On the side note, people do warm ups so they don't have to injure themselves. Pieces that are incredibly difficult or fast require a warm up so the hand gets used to the instrument. You can't start out playing fast right off the bat, you could get cramps. Also if the weather gets cold, people do warm ups (as the name states) so they could get their fingertips moving.
Musical performance is analogous to athletic performance. It takes lots of practice. Warming up is important to avoid injuries (more repetitive injury than broken bones in music unless you move your own pianos).
Playing scales and chords is important, especially in all keys. (It's like hitting a tennis ball against the garage door or batting against a pitching machine.) Much of piano music of all types consists of chunks of scales and chords. It also helps with sightreading as one can see an Eb-Major scale part rather than just "some closely-spaced notes."
It's also important to play pieces you like (that's a big part of enjoying music) as well as pieces which help to improve technique. Some sightreading is import too.