This is just my experience as an over-thinking introvert and not every single DM will be able to relate, but I'm sure that not a few find the task absolutely exhausting.
After every session, my voice and nerves are shot. I've just spoken nonstop for five hours, which is more than speaking than I do all week in total. I try to be concise, of course, for the benefit of the players, but I often end up giving long answers to questions and anyway must provide quite a lot of description and information just to move the game along. This isn't difficult if I psyche myself up to it with lots of espresso and the music of Arany Zoltan, but when it's all over I feel like a sponge that's been wrung out.
It precludes doing much else on weekends, and especially anything having to do with human contact. Even speaking to my wife doesn't come easily, but she understands and tolerates my monosyllabic responses at times like this. Socialising is out of the question.
For example, I have a neighbourhood obligation on Sunday nights which I'm inclined to cancel on the days we play, even though it's several hours after the session has ended.
I bought a house in a village in Japan, where neighbours are closely knit and expected to all do their part in the community. The man who lives across the creek could hear me practising the flute in the morning and decided that, for the upcoming lion dance that takes place around the district next month, I could apply my efforts to the traditional Japanese transverse flute. All the non-elderly men in the village participate. It would have been bad form to refuse, so each Sunday evening I faithfully show up to practise from the hours of six to nine, which in actuality amounts more to drinking beer and engaging in that sort of crude banter normally known as 'guy talk'. This past weekend we prepared the straw sandals we have to wear, and practised for a total of five minutes the entire night. Such is human relations.
Doing this after D&D, however, would amount to an overdose of humanity. Normally, it takes at least as many hours to recover from playing as I've spent playing.
The thing is, the event is coming soon and the men want to get in as much practise as possible. I'm going to attempt doing both this coming Sunday. Needless to say, I'm looking forward to D&D more than to practice.
It's worth it, of course. Introverts are capable of being as jovial and boisterous as extraverts; we just need a long time to recover afterwards. I'm not sure I'll get that this time. It will be interesting to see what condition I'm in by Monday.