One way to lose the blower or compressor is to make the oxygen available by being part of the fuel blend. For example alcohol and hydrogen peroxide will burn in the absense of air. But this changes jet design into rocket design. It also requires carrying extra oxygen doner material, which may or may not add up to the weight advantage gained by the loss of the blower/compression.
The target I adopt the blower/compressor has two: 1. to get oxygen from air. 2. to get certain high pressure gas before combustion, that's good for efficiency. You seemed to just mention one aspect.
If the material for combustion are stored in high pressure. It is possible to mix them into a certain high pressure gas before combustion. that may be not complicated. so the portion is light.
To consider from another respect, even though the new type jet engine is heavier than the current jet, but its efficiency is higher than the current one’s. The extra weight definitely is much less the weight of fuel that the new jet saves.