You're exactly right. But as you suspect, there's reasons why you wouldn't want to do that in all cases.

Turbojets derive all of their thrust from the turbine exhaust. It's a small, compact engine, which means high power-to-weight ratio, and it's great for small jet fighters. Unfortunately, it also consumes a lot of fuel. Turboprops are at the other end, where the turbine drives the propeller at much faster speeds than a regular 4-stroke engine would. But the exhaust provides next to no thrust.

Turbofans sit in the middle. They provided much better fuel efficiency than a turbojet but greater power than a turbofan. It was very much a "we need a middle solution" type of engine.

As turbines became more efficient and compact, the turbofan became smaller as well. To the point that they could be places on a fighter, but with a smaller bypass ratio. This gives much better fuel efficiency (range), while still retaining high power.

For jetliners, it's all about efficiency, but still retaining a degree of speed. But for a really high-bypass turbofan (50% or more), it's going to be a huge engine. Fighters are between 15-20% now, but you won't see much more than that.

https://en.wikipedia.org/wiki/Bypass_ratio

Tom Clancy wrote a book many years ago in which he discusses this in laymans terms really well: http://www.amazon.com/Fighter-Wing-Clancys-Military-Referenc...