Well given that the c4-f7 diagonal was an important part of my later attack, I can see that trading would be bad at least in one way. I'd be giving up an active and powerful piece in exchange for a black piece that really wasn't doing much.
At the time, my focus was on preserving the center I'd just built up. (As has been noted, I was seeing the center more as an important goal in itself rather than as space to further secure an advantage.) So my thought was to keep the tempo I'd gained by not doing anything which would allow black to freely develop. I was focused too much on preventing the g4 pin, which I later realized was far less powerful than I'd thought it would be.
Had we we exchanged pieces, I was thinking the line of play would look something like this:
9. Qd3 Nxc4
10. Qxc4 Be6
11. Qb5+ c6
12. Qh5 Qd7 (or perhaps Qf6?)
13. Ng5
I would also move the bishop to b3. More space, better development, the possibility of mating him in under 10 moves, nope, I am not exchanging pieces.