Does it really spare you a hotel stay?

With a plane, I leave at 10:00 in the morning, arrive at say 14:00 in the other city and check into a hotel at 15:00.

With a train, I leave at 22:00 in the evening before, arrive at say 10:00 in the other city and check into a hotel at 15:00.

Same amount of hotel stays. A few more hours in the other city. But since I have to carry around my luggage and don't have a shower and toilet, I am not sure if those hours are a plus or a minus.

Leave at 10 pm, arrive at 8 am in Austria, connecting train to a village in the middle of the Alps, get some last minute supplies, start hiking at 10 am, arrive at the mountain hut at 5 pm. Not really feasible with air travel without spending a night in the valley where you don't actually want to be as 2 or 3 pm is too late to start the hike. Admittedly that is a very specific example.

For city travel, I've had good experiences with hotels that let me check in early (before noon). I've never had a hotel that wouldn't let me stash my luggage before check-in.

Obviously depends on the user. When I was younger I tried the night train thing on a trip that hopped a few European cities. So, stay in Munich for 2 nights, then on the 3rd night, get on the train to Vienna. Stay in Vienna for 2 nights and get on another train ...

Basically spending 2 out of 3 nights in hotels due to the night train (compared to if we'd done the same itinerary but with daytime trains).

You're missing a night somewhere. Day 1 10:00 - Day 1 14:00 means you need a hotel room Day 1. Day 1 22:00 - Day 2 10:00 (more like 6:00 IME tho) means no hotel room for Day 1.

Train stations in Germany at least generally have luggage lockers, so you can just leave your stuff there. It's not hassle free, of course, but pretty convenient. Not sure if that's common in other countries.

Quite a few of the night trains I've taken have had showers. Sometimes shared per car, but in the more modern ones usually in the cabin.

Night trains really are the closest to teleportation that humans have come up with yet.

Back in the old days when I traveled for work, I had to be in the other office at 9am, which meant I would travel the previous afternoon and grab an extra night at the hotel.

Even with your example, you're getting an extra day in your destination without an extra hotel stay.

The point would be to skip that hotel stay alltogether by arriving the next day. If you have things to do during the afternoon the day before resulting in an extra night then it will not save anything.

you can a)leave your luggage at the hotel early b) use a locker at the train station to store your luggage c) avoid bringing a lot of luggage for this trip

You assume you were at home before taking the plane or the train. Sometimes you'are travelling from one hotel to another.