AdamFrisch
I would however argue that the fan jet at the front is nothing more than an low pressure air shifter similar to a prop. It's not part of the turbine. In fact, the blades are often made out of composites as they never get hot and it's sole purpose is to give thrust by shifting big masses of air around a turbojet core.
As for the validity of the bigger/slower vs smaller/faster of airflows, I've been told that bigger/slower is more efficient for some reason. Don't really know why. But in helicopters (which I have some slight experience with) the bigger the rotor the less power it needs, that's a fact. It also gets quieter the bigger it gets, which makes sense. But a slower rotor also stalls quicker, so it's a balance (not really a concern in a fan jet design).
Most new helicopters have pretty small rotors with high rotor disc loading. This makes for fast and nimble helicopters, but they're very power hungry.
Interestingly, the abandoned propfan concept where the blades were unshrouded did reduce fuel consumption by 35% (compared to 90's turbofans, that is), but it did produce noise problems. Apparently in these fuel crisis times, engine manufacturers are taking a renewed look at the propfan concept.
Your questions are fine for a technical forum, however your presumptive statements of fact have a tendancy to turn off a responder since to respond implies either an acceptance or an argument first.
The design engineer can achieve simple soultions both by gearing between the fan and the turbine as well as by use of variable pitch blades. Both have been done in experimental type gas turbines. However there are lots more considerations or balances between competing requirements that need to be addressed in order to make a viable product. Not the least of which is comparable safety (certified standards).
As for the products currently in the marketplace they have also had to meet a cost of ownership standard which includes maintenance consideration (how long and how much cost)
As for bigger engines one of the pinch points is still the landing gear and its length to keep the engine above the ground.. Yup you can put the engine above the wing but that has its drawbacks as well.