But that's just it--the puzzle ceases to exist once the interface becomes point-and-click, because the original puzzle is just a basic keyboard dexterity puzzle (early graphic adventure games were rife with them, especially the Sierra games, as we all know.) Now, that type of puzzle really can't exist in the same way in point-and-click. It just doesn't work. Sure you can click off the edge of the cliff and Alex will step off to his doom, but that's not really something you're going to do by accident--you have to purposefully move the mouse off the path and click. I don't remember if IA put automatic pathfinding into that area or not--I wasn't part of the team when KQ3 was being developed, and it's frankly been ages since I've played the remake. But I do know that we have a basic philosophy when it comes to translating obsolete keyboard-based dexterity puzzles into point-and-click in our games (there are a handful in SQ2 that we had to tangle with also)--and that's basically to scrap them completely and come up with something else in their place.

In the case of KQ3, once that screen loses its purpose (i.e. you walk down the mountain the first time) having to go back through that screen when you want to get back to the house is just a needless delay.
Now personally, had I been on the team back when we were doing KQ3, there are actually a number of other things in the game that I would have pushed to do differently--namely, I would have made it so the player has to physically combine items to create the spells, just like the KQ6 system, rather than having the spells be able to be automatically created once you had gathered the items--it would have allowed for more death opportunities if you combined the wrong items, and in my opinion would have been a little truer to the spirit of the original, while still removing the silly element of copy protection (typing the exact commands word for word from the manual.) I also would have put in a command to bypass the waiting (because of the point-and-click interface, the clock pauses every time you access the command bar or inventory screen, so you can actually complete the needed tasks when Manannan is away much MUCH faster than you could in the original game--so if you want to see the extra easter egg scenes and stuff you have to do a LOT of waiting.)
But anyway, as far as the mountain path thing and the map taking you straight to the top goes, it was done for expediency's sake, since the path screen loses its purpose after the first time you go through it. I think it was a reasonable decision.

I think a lot of people confuse the term "remake" for "graphics and sound upgrade," and expect only ONLY those two areas to change when a group undertakes one of these projects. Personally, I think that sells the whole process short. The point is to really improve the playability of these games in numerous different ways--yes, that means a graphics and sound upgrade, but also it means removing obsolete puzzles and functions, particularly those that don't work in point and click, and even in some cases expanding story elements to make for a fuller and richer experience with the same tone and atmosphere as the original. 1:1 remakes shouldn't even be called remakes, in my opinion. It's just a facelift.