The new Toyota/Subaru sports car even uses a combination of direct injection and injection just before the valve (called “port injection” because it fire into the intake port). It allows the engine to take advantage of the attributes of each.
But for every squirt of fuel you need the equivalent of about 14 squirts of air to create combustion. The process of combustion is the hydrogen and carbon atoms in the hydrocarbon (gasoline) tearing themselves apart and bonding to oxygen atoms. For that you need the oxygen, which comprises about 22% of the air. You need the air. Thus, you need a system to get it in the cylinder, and the best that’s yet been developed is intake valves.
For the record, that need for the hydrocarbon molecules to be in contact with oxygen to burn is the very reason fuel is vaporized. If you light gas on the ground, only the vapors and the very surface molecules burn. The gas under the surface actually doesn’t burn until the layer above it is gone, exposing it to oxygen.
And then you need to get the burned fuel (now gasses) out of the cylinder. Again, the best idea so far has been valves.
Although, there was a small design firm some years back that came up with a constantly rotating shaft with holes in line with intake and exhaust ports, like a string of ball valves, that replaced the traditional valvetrain and all it’s reciprocating masses. He developed it to a working prototype. I always wondered what happened to that design. I assume it wasn’t deemed durable enough long-term to put on the market.
By the way, I like the way you’re trying to figure out how things actually work. That’s my way of thinking as well.