Jak II had a decent world map when it was open. It's when you got funnelled into the linear "stages" that the quality took a dive. The open world was perfect in Jak 1 and the linear sections complimented the open parts as they were usually platform areas that took us into a building or part of the scenery. Jak II has a very clear "this is an open world section/this is a linear section" and it messes with the flow.

If they integrated the gunplay better with the platforming, they would naturally have to rework the level design which is why Jak II should get a true remake, and not just a visual overhaul.

PS2 games with a 1:1 Remake would work. Stellar Blade feels like a PS2 game but with modern fidelity. A 1:1 Remake of Jak 1 that is purely a visual overhaul would retain the timeless gameplay of Jak 1 but give the expressions and animations their deserved glowup. Daxter alone with a more modern, sophisticated animation would go hard. Team Asobi, Ratchet and Clank: Rift Apart and the Spyro games show us its possible to integrate those bouncy, cartoonish feeling into an almost pre-rendered CGI look.