I'll go out on a limb and say that allowing arbitrary saves is detrimental to game play. By limiting saves only to between levels (aka when on the stairs), it negates the need for the player to remember what was going on in the map prior to the save, particularly when the next time the player loads the game, it might have been days since then. Giving the player a clean slate (or level in this case) is beneficial for the player -- no need to remember what was going on other than the challenge mode activated and the build one is striving for.
DoomRL is a fast-paced game, compared to other rogue-likes. However, "fast-paced" here does not refer to having to move all over the map at a frenetic pace -- it means that the total time required to complete a run is significantly shorter than that of other rogue-likes. There are no quests, no fixed special item that you need, no long drawn out levelling up process, no item crafting, no shops, nothing -- that's what was meant by fast-paced. Sure, one can take 20 hours to figure out the next best move via alpha-beta pruning, but as far as the game play goes, it's still fast.
The last thing to note is that for DoomRL, completely exploring each level is not a prerequisite to winning.