The US used to operate like that. They operated escort carriers and fleet carriers both.
The small escort carriers back then were used to guard other ships against submarines. Right now China has a similar problem in that the US has superiority in terms of numbers of submarines. The smaller carriers would enable building more of them. They would then have anti-submarine aircraft in them. The question is if something like the Type 076 would be enough or a larger flattop would be warranted. In case that kind of strategy is pursued in the first place.
The US operated escort carriers during WWII as a way to escort supply convoys across the Atlantic (hence the name). Air cover was necessary as they sailed beyond the range of land-based aircraft. They were a cost-effective solution for a misson profile which did not require the speed, airwing, or other capabilties of an expensive fleet carrier.
How many convoys is the PLAN expected to escort beyond land-based cover in any future high-intensity conflict?