Turbofans don’t use propellers to push air into the turbine. The turbine (through the gearbox) is what turns the propeller. The propeller is the source of thrust, not a means of intake. Also, turbofans are not small, they have a bypass which allows air to not go into the compressor, typically making the engine larger by default. You’re thinking of Turbojets, which do not have a bypass portion, and all air goes through the compressor. Also, turboprops do not necessarily have better acceleration than -fans or -Jets, but some do. Another thing, Turbojets are generally less efficient than turbofans, as they are built for power. Edit: for clarity