yeah, my Model T starts to get dirty at about 3 on the volume knob, not really a clean amp at all, but a great one.
Yep - and you'll find that to be true about all original model T amps - even the second generation.
Tube amps, especially the model T, have never had any great amount of headroom. It's the nature of their design.
The tube stages on most any amp are essentially running "wide open" - fully bypassed cathode resistors, no local feedback, high value plate resistors - anything and everything to get the most gain out of as few gain stages as possible. It's an economic thing.
In most tube amps you will find only two or three gain stages before the power amp. Amps with more stages came later, and these amps will have resistive dividers to cut back on gain so as not to overdrive the next gain stage too heavily. This causes what is commonly known as "farting".
The first generation model T only has two gain stages. It needs to boost the guitar level up to line level to drive the power amp. You can't waste gain with only two stages. What you give up by using the maximum amount of gain from a tube is... headroom.
You also need to look back at history - back when the model T was introduced (1973) consider what its potential customers were looking for in an amp. I guarantee it wasn't headroom.