Ganja -- good answer!
Real world example: flying in the southern US in the summertime, it's not uncommon to have that quarter of the continent all have some chance of thunderstorms in all the forecasts. You may have an hour's flight from A to B, but to get an alternate without the chance of thunderstorms you might have another 3 or 4 hours to get there. BUT, the CB's aren't everywhere, so you file what you can & away you go. You get to your destination, only to find it covered with a massive but unmoving CB. Time to go elsewhere. Find someplace clear & desirable (from a perspective of facilities / equipment / accommodating pax / company presence / good pilot lounge / whatever), and go there. If what you'd filed as your alternate is, at that time, ALSO looking at a big lightning show, you discard it from consideration & press on with your decisionmaking process... I've got X fuel on board, and I can get to the following fields with my 0:45 (or whatever your book says) reserve... what's the smartest place to go?
You would NOT tie yourself to keeping fuel to get to your divert AND from there to your filed-but-useless alternate in the tanks! You do what makes best sense at the time... it would be silly to, for instance, restrict your consideration of divert fields to only those that are close enough that you could divert there without burning into the "and get from here to (someplace we aren't going to really go)" fuel.
Alternates are for FILING purposes. Dispatchers also watch them a bit during the course of your flight so that, for instance, if one goes down they can come up with a new gameplan (revise the release, make YYY the alternate instead of XXX, etc). HOWEVER, the filed alternate is IN NO WAY restrictive of your options if you find yourself needing to divert.
As for declaring Emergency Fuel, if you as PIC see yourself as having a critically low fuel state, then by all means declare it. However, if I'm diverting to a field with reasonable weather and I'll get there with my 0+45 reserves (or whatever amount you're required to have overhead the alternate), I wouldn't see any point in declaring emergency fuel nor even min fuel, simply because by the time I get there I couldn't do a SECOND divert to the "filed" alternate.
For the original question, I'll offer this: a release can be revised in flight, and the book I fly with doesn't restrict that removing an alternate can NOT be a revision... so I'd say there's nothing preventing it. For most operations, there wouldn't be an advantage to it, although I can think of one oddball case where it would: operating to a remote destination with a somewhat distant alternate, the destination weather goes from low overcast to clear (& forecast to remain that way) sooner than expected, while the alternate goes from okay to below mins. From a dispatcher's perspective, there might be an advantage to revise the release based on the new conditions (alternate not required) rather than try to formulate a gameplan based on dealing with an alternate that's now unusable... particularly if such a gameplan might require an expensive option like turning back or some such. Not generally a factor in domestic operations, but might be a player going to remote islands or somesuch.
