1. What is the idea?
One of the frequently proposed ideas is simply that the unit advancements go further. This was turned down for one reason, and one reason alone: it isn't interesting.

Well I personally find it interesting. Enough people did that it became an FPI too. It doesn't actually hurt the game in anyway.

2. Why do I want this?
I like having veteran units. I get attached to them honestly. This would allow them to get more powerful (assuming I can keep them alive). It's just fun. It plays to that "gotta unlock everything" urge that most gamers have.

3. How exactly does it work?
Well I know this isn't as fancy as new hardcoded ground breaking features, but I feel it's within the Fork's goals. All that has to be done is to create more units.

Fortunately someone has already been working on this for quite some time. Ancestral created the Ascension Era.
http://forums.wesnoth.org/viewtopic.php?f=19&t=26388
He has a lot of the units up to level 5 already.

4. What are the advantages?
More, more powerful, units.

5. What are the disadvantages?
It lacks art for the new units.

6. Other thoughts.
I would love to see this replace default so that it can be used in all the SP campaigns. Higher level units don't ussually have to be balanced. As far as I know the current level 2's aren't taken into much account when balancing, and level 3's+ aren't really cared about at all.

If a full replace isn't wanted, it woulds still be trivial to add this as an optional era, and perhaps make modify the campaigns to include an option in the first scenario to "open up the full unit trees". This would set a variable (variables persist through scenarios) that is checked whenever modifying the recruit lists throughout the campaigns.