Certainly, straight up removing the questionnaire is the easiest way by far. I do have a few thoughts, in rough order of radicalness:
My impression of questionnaire generation, the few times I used it, has always been "wow, this is a lot more questions than I expected". Simply reducing the number of questions on a given try might help.
Some of the answers feel like they should have an impact on your alignment - when you do something clearly chaotic like betraying someone, for instance. The possibility of alternate or additional effects of answers has been raised once or twice above.
The impact of your answers on your stats is fundamentally rather invisible unless you consult a table compiled by people who've put the time into examining the system. More transparency here would both help the player make an informed decision and show the player that their decisions here matter and have a tangible effect on the character. ADOM places a lot of weight on figuring out hidden information through trial and error, but in the questionnaire system this is heavily obfuscated. The simplest way of adding transparency here would be to just show you what stats you gained up front, or in a screen after the question - see my next thought.
What if you had a small number, something like three to five, vignettes from your character's past (probably based on the questions available now) presented to you, and then based on your answer got a screen with a short summary, a sentence or so, of what happens afterwards along with a note of the benefits you got, which could be bonuses or penalties to stats, an alignment penalty or bonus, extra gold or less gold, a modification of your starting inventory, etcetera, tailored to the scenario. If you help out a merchant who then rewards you, you might start with extra gold, if you studied under a wizard you might have a random potion to start with or even a free reading from a low-level spellbook with the right answer. The small number of questions does several things here:
It makes it easier to balance the addition of non-attribute bonuses or penalties by reducing the gap between your beginning and end states, allowing you to tune the tradeoff between attribute points and other effects with the knowledge there will only be a few. It also makes the balance less important, because:
The smaller sample size increases the variance between individual questionnaires, making it less attractive an option for pure optimization, as you can't guarantee you will even get the option to influence your character in the direction you want. The potential of benefits you can't get from other creation methods means it's still possible for players who are interested in that to want to use the system and optimize their choices.
It redues the tedium and barrier to entry of the system, naturally.
Finally, the limited number of questions combined with the active, visible feedback you get should make the choices that much more memorable for players who are into the roleplaying aspect.
Now this would be much more work than just excising the system altogether, obviously, so I definitely wouldn't blame you for going ahead and doing so, given it's ultimately a pretty small part of the game. I do agree that its current state isn't ideal either way, especially with point-based creation taking away the aspect of giving a player more control over their character's attributes.