In a sense, the notables ARE the population pool, albeit a relatively shallow one. For instance, Aserai starts the game with something like 8 towns and 40 villages. If there's an average of 3 notables per village and 5 per town, then that's a pool of 160 troops that they have immediate access to (as long as they have high enough relations). The amount of notables a town or village has can grow or shrink with prosperity and hearths respectively, so a faction's total population pool can vary depending on how strong/prosperous they are as a whole.
If a faction is at peace or is dominating a war, then they will not be expending many troops, meaning their pool of recruitable troops should remain high, and the troops in that pool will be stronger from upgrading over time. If that faction enters a war or starts losing, they'll have a buffer of higher tier troops on standby that they can quickly draw from before they start to feel the effects of war.
Conversely, if a faction is struggling in a war, their notables' pool of troops will be drained, and they will have to rely on the daily rate of troop production of their notables in order to supply troops to keep fighting. The lords will spend more time bouncing around between settlements trying to scrape up what's generated each day before their other faction members do, thus hindering their ability to put up a resistance.
Basically if the rate of expenditure is greater than the rate of production, then the pool will eventually be drained and the faction will be restricted to how many troops can be created in a day. If the expenditure is less than the production, then a faction will not be limited (as much) by how many troops are created each day. Most other games with population systems have this same dynamic of being limited by per turn production if they hit the bottom of their pool, they just have deeper pools, so the effect of hitting the bottom is more stark. Bannerlord could be pretty easily tweaked to be more similar to other games by simply adding more total notables and reducing their daily rate of production so there's more of a difference between a full pool and an empty one. As others have said, that might just lead to more snowballing if the AI couldn't be made to properly manage it, and it's personal preference whether or not that's a good thing.
So essentially this game does have a population system already; it's just integrated into the sandbox as npcs rather than abstracted as a number in the corner in the way other games do like: ? 1000 (+20). There are still some meaningful differences though, such as lords having to physically visit a location, rather than just queuing up new units, as well as there being a maximum population represented by total notables' slots. Garrisons also act as sort of an extension of population pools.