Is there any reason not to dismantal all research stations after you've completed all research?

While you may have researched things already and won't need to re-research them should the research buildings be destroyed and then rebuilt, you will not be able to build things that are dependent on research if you don't have the required buildings.

In other words if you destroy your research stations every research you done will go bye bye

Is every tech effected by this.

eg the eco upgrades, if one has 3 civstations and has researched some metal upgrades is this rate increase lost with the loss of the research stations.

or the enemy fleet incoming tech, is this too lost?

As far as I know the only effect of losing research stations is that you cannot build structures and ships that are dependent on the research.  I don't think you can fire Level 8 superweapons either (the sailors manning the super weapons just "forget" where the big red fire buttons are located at), though this is really only an issue for the TEC since it doesn't make sense to build the "super" weapons for the other two races.

For example, if you are Advent and you have a total of 3 Weapons Labs up and you've already researched Illuminators, if you scuttle one of the weapons labs (or if one gets destroyed) leaving you with 2 weapons labs then you can no longer build Illuminators until you have 3 weapons labs again.

CenturionJixra is correct

Research that grants upgrades or abilities is not affected, it's only new structures, ship hulls, and superweapon building/firing that need the number of labs maintained.

You also have the benefit that for each research station you build, corresponding ship and structure construction speed is affect also. If only by a small ammount per station, it all adds up.

Actually, I have found that the Advent cannon is extremely useful if you know how to use it right.  It is not an automatic game breaker, more of an economic warfare tool mixed with an early colonization aid.  the tricks you can pull with this, ranging from devastating the tax/mineral collection of the enemy homeworld (and by extension, every single planet with more than 35% loyalty because of it) to rendering captured planets immediately colonizable, assisting with moving your capital forward for a push on an enemy home system.  Getting combat bonuses in massive fleet battles.  If you do not use culture to your advantage, you are missing half the fun of Advent.  It is not as direct as 'goodbye population' but can be every bit as nasty, maybe more so.

I also like the Advent cannon.  With the correct research, if you keep a steady stream of fire against an enemy planet you can cause the population to rebel (loyalty drops to 0) and the enemy loses the planet.  With a strong enough culture and good use of Advent cannons, you can even win the game without sending your ships outside your own territory.  Of course, that's not quite as much fun as nuking the universe, but it does bring some variety!