They help increase your military value, and therefore AI's dont pick on you and start wars as much. Also, stacking them, while costly, really boosts your military score and your final MV score (if the metaverse matters to you).

And at least once you should build like 20 of them and add all the +1 speed modules and slingshot your ships across the entire universe in 1 turn. Thats always fun!

I seldomly build these at all. It seems their main use is in increasing ones military score. However, thats not to say the are useless, they do provide the ship assists you mentioned. This can be good for fleets of smaller ships, but even then only at the stage of the game before super ships are flying around. You, know the ones with over 500 attach and defence; not much +1 to lasers will do to help.

Since they are stationary they are even less uselful because the area where you are fighting will soon move on, leaving the starbase doing nothing. I used to build them more but found my offensive onslaught moved faster than the constructors.

Where I DO find these to bu useful is in the negtive meovement to enemy ships, and the pluses to my own. As the Yor all AI shjips automatically have a maximum speed of 3. Add a -2 speed modual and my enemies are now moving at ony 1 pc per turn (as long as their turn started in the influence of that startbase). THAT is the best protection your planets can have. I built a sting of starbases along my entire border fot this purpose.

So basically they are not worth the number of constructors ofr the research time, unless you have a specific area you want an offensive boost in or to have additional defence in.

IMO they're not really that great, although it depends on the situation and your race.
For example on tiny+small maps they can be worth consideration, since you don't need so many to cover your planets. They're also good with say the arceans since they have access to cheaper constructors, and of course with evil races who don't have upgrade costs. However I'd say actual combat use of them (in my case) tends to be restricted to a specialised strategy where I use stacked military starbases coupled with tiny/small fighters (depending on my miniaturisation) with 1 attack and 1 defence - due to their incredibly low cost you can produce swarms of them and overwhelm your opponent, providing you have a high enough logistics ability/advanced enough starbases.
I might also build a few in the early stages where I don't have the techs to get decent combat ships and so build constructors instead.