Unfortunately we're sort of stuck with a hybrid situation. The ship system seems to be designed from an end-game-tech point of view with ships intended to have differing roles similar to 20th century navies. The tech system however doesn't really go along with that idea. As OP says, historically all ship classes got bigger over time; we didn't invent patrol boats, then destroyers, then cruisers, then battleships. If anything it was the other way around: build the biggest ships you can support first and when they get too big to use for some tasks you invent smaller classes for those tasks.
EDIT: If you wanted a more historically-oriented tech tree you could probably introduce all the ship types from the start but with new sections becoming available over time with more and more weapon and aux slots.
I love your description of the development path. I also agree with the idea of having all four initial classes at the beginning, as I'm never entirely married to any of the dozens of ideas I've thrown out there over the years.
I put together an idea for starting all of the classes with a default same-size-slot loadout (e.g., Corvette all S-slots, Destroyer all M-slots) and then unlock techs that allow for consolidating slots to make bigger ones, switching slots from utility to weapons or vice versa, and finally adding new slots on either or both sides. I could easily see that integrated into this other idea, starting the game with the smallest configurations and working up to larger ones, both by slot size and quantity of slots.
With that, you could keep the same four classes, while allowing each to get bigger, stronger, and tougher through the decades. You'd have to pay more for ships built with the newer hull sections, but they would allow for higher speeds, max Evasion, Hull Points, etc. A more advanced stellar navy would have cruisers that are easily a match for another empire's battleships. As with anything else, you'd have to make a ton of parallel changes to make it work, but that could open up a number of other improvements and fixes at the same time.