What would be the issue/effect of having the bridge too far away from the nut on a large fretboard with standard fret sizes? For example, a 24 fret board with 25.5 inch scale fret spacings, but a bridge 28 inches away?
All the notes would play flat (lower in pitch). The 12th fret (for example) should normally be halfway along the string, so that it sounds an octave higher than the open string. If the bridge saddle is further from the 12th fret than the nut is, the 12th fret would play a pitch lower than the octave above the open string.
The fret spacing (distance of each fret from the saddle) is very precise for any given scale length. Many guitar manufacturers stick with common scale lengths so they don't have to constantly re-calculate the fret spacing. But the scale length varies between guitar builders and some even offer options for different scale lengths.
Moving the bridge even a tiny bit will totally change the intonation and result in a new tuning that will not sound correct with any other instrument. You will be able to get one fret to play in tune, but all the other frets will be out of tune.
Even guitars such as an arch top that have a movable bridge must have the bridge located in precisely the correct location. If a movable bridge gets knocked out of position, and there are no markers on the top to aid in placing it back in the exact place where it is supposed to be, then you can find the correct place by playing a harmonic at the 12th fret and comparing the sound with a fretted note at the 12th fret. Keep moving the bridge until both notes are the same.
The only way to get the guitar to play in tune if you move the bridge is to move each fret to the precise location it will need to be in for whatever new scale you create.
You could use a neck for a baritone guitar which is set up for a longer scale and place the bridge in the exact spot for proper intonation, checking with the 12 fret harmonic method mentioned above.
An experienced luthier will know the mathematical formula to calculate the exact fret locations for any given size scale. But in order to make that work with standard measuring devices, there are probably numbers that work better than others for scale length measurements.
As already said, this will completely change the tuning on all frets. So, the only way this could be usable is if you want to play in a tuning other than the western standard 12-edo. If you move the bridge only slightly, the lower frets will still make up an approximately equal-tempered tuning, just with another step size. Making the scale a bit shorter could thus give you an 11-edo tuning – 10-edo would already be problematic because the higher frets stop giving the same frequency ratios. Increasing the scale could give you 13-edo and 14-edo.
All those tunings are pretty exotic, I don't think you'd likely have much fun with them! Though there is one tuning you can achieve this way that I find quite fascinating. It's not an edo-tuning but an edt-tuning like Bohlen-Pierce (i.e., it does not have octaves at all, only tritaves). It is the 17-edt tuning.
I actually have a guitar modified for that tuning, by inserting a secondary “bridge” over one of the pickups:
An example of how this can sound:
You could possibly get this to work by having a temporary bridge - possibly just a piece of wood with an acoustic guitar saddle strip - resting on the belly of the guitar. It would be held in place by the string tension. It would be necessary to take out the existing bridge saddles etc. The rest of the bridge would remain to anchor the strings.
It would be extremely ugly though! You would have to forget about using your tremolo, if you have one.