Does anyone leave their amp and preamp on all the time?

When there’s a convenient On and Off switch—no. It only takes about 20 seconds for the tubes to warm up where the system is playable even if it’s not "optimal", and I suspect it’s about the same on most systems. If I’m not directly listening, I consider it an unnecessary waste of energy, and I’m paying for it, society is paying for it, with its impact on the power grid, as minor as that might seem—it's cumulative among different households. I also turn out lights in any room I’m not in. I consider expensive high-powered amps a luxury rather than a necessity, and I feel better when using energy responsibly. 

The issues you'll run into are primarily reduced longevity of certain electrical components. Unless it's been upgraded, your Bedini 25/25 has electrolytic capacitors in the circuit, which contain a liquid electrolyte inside that eventually dries out. Lifespan is dependent on usage, operating temperatures and quality of the cap.

This person had to replace them in 2013 on his Bedini to fix a humming issue. https://forum.audiogon.com/discussions/repair-of-bedini-amp

So, if you don't mind the increased costs associated with the convenience of keeping your equipment running all the time, it is really up to you. I keep my stuff on if I am going to be around for a while, turn it off when I know I'll be gone or unable to listen for a while.

Vitus Integrated amp stays on in Class AB all the time.  I listen in class A then switch to class AB after listening.  It takes hours to sound at its best from cold if I move it to standby.  Vitus CDP/DAC is on all the time too.

I leave all the components (pre/power and CDP) on in the the secondary Naim system at all times too.  This system has been switched on continually for 20 years!

Lyngdorf 2170 on 24/7.  Best sound by a wide margin. Takes several hours to sound its best after turn on...I just keep it on.  Less stressful on internal parts than on/off cycles.  It is a digital powered dac and runs very cool consuming only 22 watts or so.  

Anything that’s not tubes or class a I leave in all the time. Longest component I owned was an Odyssey Stratos amp that I had for about 15 years and pretty much left it in the whole time. Was still rocking when I sold it.