The input noise of a tube is like a 10K resistor.
The output of a general-purpose tube is about 10K.
The impedance of a ribbon mike is 0.1 ohms. Impedance of a dynamic mike is often under 100 ohms. Impedance of a condenser mike is many mega-ohms.
The "best" impedance for a long cable is 100 to 500 ohms, depending what factors are important. For short cables, you can ignore that: a 10-meter (30 foot) cable can be treated as a 1,000pFd capacitor which is about 10K ohms at the top of the audio band. But when you get into kilometer/mile-long cables, the cable WILL act like a low impedance and you need to be able to drive it.
So 0.1 ohm and 10 ohm mikes are, in music studio use, transformed up to 150 ohms to feed the line, and condenser mikes are buffered down to 150 ohms on the line.
Then, to overcome the tube noise, we transform up to 10K to overwhelm the tube noise. (Old PA-system mikes were sometimes transformed-up to 50K ohms to drive short lines directly into a tube.)
So you "need" an input transformer. A standard dynamic mike directly into a general purpose tube will give a noise figure of 15dB or 20dB, Soft sounds, audible in the room, will be hidden under tube hiss.
Also a tube input is unbalanced. Mike signals are weak. Even a small amount of electric noise near the cable will put buzz in the cable and the signal. We usually want to run mike cables balanced to reject buzz.
At the output: you can drive short cables with the 10K output resistance. But long cables need lower impedance. Also some recording equipment has 600 ohm inputs (because they assumed large professional studios where everything might be connected with long cables). And again, you may wish to use balanced connections to reject buzz.
You can reduce tube impedance, by using a bigger tube eating more power supply current. A transformer input tube mike preamp's first stage usually eats about 1mA. To get low noise without a transformer, we need 30mA to 100mA, which forces you to use several tubes in parallel.
You can use two tubes to get a balanced input. But the noise of the two tubes adds together. To be balanced AND low-noise, we need four times the power supply current, 100mA-200mA.
The same at the output. Any of the loudspeaker output tubes can drive 600 ohm loads if we flow about 40mA through the tube, though it may sound a little strained. Two tubes can make a balanced signal, but we need double the supply current, and many 4 times the supply current for low distortion.
Two transformers and two tubes can make a good mike preamp, eating about 5mA. That's 1.5 Watts of plate power and probably 2 Watts of heater power, under 4 Watts total.
Without transformers, we need more like 400mA for good low-noise balanced input and output! Plus all those fat tubes will need a lot of heater power. We can reduce the plate voltage a little, but not a lot. Maybe 80 Watts of plate power and 20 watts of heater power, 100 Watts total.
It almost always makes sense to buy the audio transformers than to buy such a large power transformer and suffer all the heat that would come off of a good transformerless mike amp.