The only problem really is with a 24-fret neck, you're moving the neck singlecoil back a bit, maybe 1/2" to 3/4." Whether or not it's critical to have the neck singlecoil "right under the 24th fret harmonic node" or any crap like that is actually true, there's no denying that shifting it back maybe a third of the way towards the middle position is going to change the tone a little bit, and give it something that isn't QUITE as fat and round as your classic strat neck pickup tone, simply because it's capturing a different part of the string.
For some people, heck, that might even be desirable. It's definitely not a reason NOT do do it, but rather another reason (along with body wood, neck thickness, bridge, nut material, etc) why you shouldn't expect it to sound exactly like a Fender when you're done.
Never tried it, but I would imagine basswood actually handles singlecoils well.