For MoO 2:

All your ships auto-upgrade to the best drive tech and targeting computer available to your empire when in a friendly star system. Your newly built ships automatically install the best armor and shields you have available, but only once as they leave the shipyard. If you want older ships to improve their armor or shields, you need to refit them at a friendly planet.

Every time you research something new in a particular school, (almost) all the previous technologies you have from that same school miniaturize by about 20%. Each tech can be miniaturized up to 4 "steps" like this, becoming radically more space-efficient. Plus for most weapon systems, each miniaturization "step" enables some nice bonus features to that weapon, like auto-fire (fire multiple times per round), no range dissipation (always inflicts max damage no matter the range), armor piercing (ignores targets armor), etc. So even if you wanted to use the starting laser tech on your ships throughout the game, if you don't design new ships, you never see any benefit from this extra available space and weapons perks. It is pretty easy though to click on ship design screen and simply max-out the weapons into the available space each time you "tech up".

Missiles do not auto-upgrade, and earlier versions quickly become obsolete as shield technology improves. Also miniaturization adds perks to your missiles like ECCM (more accurate vs jamming), Fast (quite a bit faster + improves accuracy), MIRV (multiple warhead 4x base damage), and EMG (single missile has a high chance of taking out target in 1 shot). SO your missile ship designs quickly suck if you do not upgrade them.

The only weapon system(s) that auto-upgrades with new technology is fighter bays / bomber bays / interceptor bays. The bays themselves never miniaturize (they always take up 30 space units). Instead the bays always upgrade their engine and armor to whatever the mothership has, Fighters/Interceptors auto-upgrade to the best laser weapon system allowable (only laser, mass driver, fusion beam, phaser or particle beam) when in a friendly system. Bombers auto-upgrade to the best laser and bomb available. Particle beam is a non-researchable tech only available if you defeat the Guardian at Orion or board and capture an Antarean raider (very difficult), but it does a base damage of 30 iirc so remains viable even into the late-game.

If you don't upgrade your ship designs, you won't be able to take advantage of all sorts of cool and useful defensive systems and "special" weapons like heavy armor (cancels armor-piercing rounds), inertial stabilizers (faster turning speed), battle pods (more space available), cloaking device, tractor beams, Assault Shuttles, etc. Also, certain techs completely neutralize certain weapons, so if you are using one of those weapons against said defenses and refuse to upgrade your ship designs, U R dead.

BUT if you REALLY don't want to mess with ship designs, use fighters. Your motherships will be glass cannons, but it is a viable ship strategy for hit-and-run tactics. BUT you still need to upgrade the mothership to better armor by hand if you want the fighters to have the best armor available.

The AI on the other hand is constantly upgrading its ships. The designs are similar to your own starting designs, but since the AI will be maxing out weapon systems and upgrading to more powerful technologies, you stand the risk of soon encountering a crippling disadvantage in combat.