I don't think you increase or maintain your flexibility by just riding with a lower drop. You either have the flexibility or not.
The single thing that has helped me is a 10 minute yoga / core routine. I started the routine for my back but found that I felt better on the bike on longer rides.
I actually ride the trainer with a riser block under the front wheel. I prefer to sit more upright. The main reason to get lower on the road is aerodynamics. Why not sit 2 or 3 centimeters higher on the trainer?
Will address your second point first - I want to use the indoor trainer to get more flexible, I have aims for next year and if I hit them in terms of flexibility and w/kg I'll be looking at getting a TT bike, but I won't be spending that sort cash if I don't get where I want. If I can get the endurance bike rigged not just lower, but also with some clip on bars couple times a week that'd be really good for me.
About what you were saying though - yeah,I was doing the flexibility stuff too when I started riding. The British Cycling recommended ones like the Indian knot and cat stretch. I had issues with ITB from distance running before I took this stuff up so figured I'd stay ahead of the game. Actually ITB is what ended my time running. Anyway, the missus started yoga too when she started riding, quite popular down here.
We stopped all that now. I do think if you have ITB issues you should stretch that area a lot, and aggressively take the foam roller to certain spots, but for general flexibility? I think you need a ton of time spent stretching to achieve anything. She was doing two classes a week, and I was doing the stretch routine three times a week. Did sort of help a little admittedly.
What I did instead was drop my spacers every 500 miles or so. You don't even notice it, well maybe you would if you go to a certain point but I haven't found that yet. Either has the missus. I can't actually go any lower on the S5. Like I said earlier though, it's not so simple as all that, I think newer riders who achieve good levels of flexibility and comfort can lose it faster. Really don't think you can compare a 5 year rider with a 1 year rider, even if their stats look the same on paper.
I saw a comment on the TT forums where a guy was saying it was ridiculous to expect good on the bike flexibility from stretching as time spent is so small. What the science is there I don't actually know though, so keeping an open mind about the best way to get more flexible, but I do want to get more flexible, not keep or lose my current level.