It's not unheard of. Samurai Warriors does this to the very same extent, and IMHO is one of the most compelling game modes on it. You can look to that (or some Survival Mode playthroughs) for some inspiration as well.
But you should really ask yourself, how many different ways can dungeon-crawling be interesting? Space exploration and treasure hunting? Strategy-game style battle tactics and scenarios? It doesn't have to just be you, and the stairs, and the enemies. There's a lot of different gameplay mechanics you can play into to keep the game fresh and compelling, not simply difficult. Adding difficulty is as simple as multiplying the enemies, actually.
Likewise, a game doesn't have to be infinitely long to be infinitely compelling. Sometimes starting over from scratch and recollecting your powers (differently?) can be more fun than simply exploiting them. And many people like playing games for short or custom-length spurts, anyways. What I'd suggest, where game length is concerned is an approach like so:
-How many gameplay mechanics can you come up with? And how well could two of them combine?
-For simplicity's sake, let's stick to 10s here. Let's say every 10 levels plays like so: 3 sets of 3 sublevels (IE: gameplay dynamic changes), and then a boss or special encounter, kind of like a half-baked plot that unfolds every 10th level. You may even have three or four different plots, considering.
-The number of max levels (tens per plot) should depend on how many gameplay mechanics you can come up with, and ways to keep your gameplay interesting. If you're going for replay value, you can also consider that you should have at least twice the number of mechanics as your game would use in any one, non-extended session.
-A save/continue option every 10th floor would be killer too. Or if you want to streamline it even further, you could do 2 sets of mechanics for 2 floors apiece, and then a miniboss every 5 stories, and have a shop/save/continue point there.
-Give each floor (or two... or five) *something* worth digging around to find. Don't JUST award cash, arms, or max life increases simply for completing floors and beating bosses - make players dig around a bit to get them. Keep it balanced by making it too tough for them to progress very far while avoiding all of them, but so collecting 2/3 of them or so might keep the player's ability fair with the most of the enemies' (and so being thorough may grant you a bit of an edge).
-The occasional "generous item cache" is not a bad idea, either. Perhaps once in every batch of levels, there's a sometimes-hidden cache full of one or two particular items, which will effectively "flavor" the game somewhat. It can also act as a beacon of hope for players regardless of their condition, as you never know when you'll find one or what it may contain. Hope is never lost!
-After the first couple batches of levels, give the floors some kind of serious threat that's far above your usual threshold - something beatable, but barely so. This will incentivize players to continue moving forward, and put a big risk/reward twist on exploration that keeps it tense and exciting. Maybe give the players a fair amount of time before it "awakens" so they aren't helplessly pincered by it at random; and that players in some way or another can outmanuever it, or blockade it. (It doesn't have to have a lot of HP, necessarily - it just has to have a way of doing huge damage, and incurring a major hit reaction.) A selection of different enemy types along these lines would keep things exciting, too.
-Be FUN with your traps!! These are often hilarious sources of both "yet another stupid deaths" and domino-effect delightfulness which sometimes works to the player's advantage! Both of which are key in creating "fun factor" in this type of game. Stepping on a sleeping gas tile that puts you to sleep is boring. Stepping on a rolling-boulder tile that crushes a few enemies, grazes by you, and triggers a couple other traps along the way? Fun. A trap that sends you or an enemy flying a certain direction (and tripping any traps along the way) can have plenty of fun (or fatal!) outcomes as well. You don't need a lot of different types - Spelunky for instance, uses fewer than 10, but to great effect.
-Give the player powers/abilities to collect... and THEN MAKE THEM USEFUL. Design your more advanced areas in ways where particular powers or items would be very effective for navigating or fighting, and even rewarding just for having and using them. Don't forget that stuff like weapons can be used for more things than just fighting enemies! Players can also have something in the dungeons worth healing other than just themselves, too.
Start your game short. Make it 10 or 20 stories long at most, and work in more details and gameplay mechanics. As you come up with and implement more design ideas, broaden your max level amount/game length accordingly; but keep options open for people that enjoy the shorter games, too.
Finally, remember that "procedural" does not HAVE to mean "random." Clearly you'll want some random factors in it, but also consider the ability for one thing to systematically create another, such as a key item creating something nearby to protect it; or a "problem" can be created along with a solvable element.
Giving the game a sense of directional flow (top to bottom, bottom to top, one side to the other) may demystify it partially in a mazelike sense, but it would also help to better organize such elements. Going from, say, a bottom-left corner to an upper-right most of the time still presents plenty of possible ways to get there. Or going from a random location on the left to a random one on the right still presents a "which way will be right this time?" predicament. In fact, basing each group of levels on a different type of directional flow can may even you get different effects from the same assets.
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