That would be a poor choice for half a dozen reasons.
1: 6L6 requires astronomically more voltage drive than a guitar can supply.
2: A 6L6 is built to "gate" or control a powerful stream of current. Similar to what I said #1, a guitar has nowhere near enough power to "turn the crank" or "diddle" a 6L6. It would as if an insect is trying to turn on the faucet in your home. It doesn't have anywhere near the strength, ot torque, or however you'd like to measure it.
3: Ergo, what we want to do in the first tube or first three tubes is to boost the daylights out of our teeny guitar signal so that it at least has some hope of trying to diddle a 6L6. Out of a guitar we have 1/4 volt, 1/2 volt. To drive a 6L6 we want in the area of 25 volts, perhaps more. So we need to multiply/amplify that guitar signal 100 times.
4: At the same time, it is massively easier to manipulate our tone while the signal is small, provided we can do without inducing hum and noise which would be amplified along with our native guitar signal.
There are plenty of "boutique" amps that use those big fat tubes as output devices. They very much tend to be Class "A" which can produce a very clean signal, but we are not especially interested in the cleanest of clean signals.
Most of them are kind of transmitting tubes, they were developed with those uses in mind. They are expensive and much harder to get.
They usually have 2.5 volt heaters at high amps which is a complete irritation since all our other tubes have 6.3 volt filaments.
They are built to have high high volts on the plates. 1200 volts, maybe. 450 volts is dangerous enough. Once you start getting over 1000 volts all the surrounding parts have to be high-voltage rated, thus they are MUCH more expensive. We really would like not to have 1 kv+ running around our amp if we can avoid it. The potential for arcing, not to mention death, is large. (Not that 450 volts can't kill you) That's one of the reasons why those tube usually have special leads going to their plates, yet another reason why just a plain old socket with no external leads is easier to deal with.
There's other reasons, but those should be enough to produce the wave-off.