Currently all my chest work is done on machines (incline Smith, flat machine press, pec deck) and everything's growing just fine.
However I only started training this way because my shoulder was busted and I wanted to experience the novelty of a pain free workout.
In normal circumstances I wouldn't rely entirely on machines purely for the sake of different implements providing slightly a slightly different stimulus, but I don't think you'll miss out on any growth from just training on machines provided you attack them with sufficient intensity.
You are correct to question this method and bounce ideas off other lifters here.
Here is what I predict will happen should you stay with this method indefinitely:
1) You'll become progressively worse at performing free weight movements. Every single session, I am consciously trying to improve my technique. Mastery takes time, patience, and FOCUSED practice.
Wait, you say you primarily care about "muscle/aesthetics"? Fair enough. But there will come a time when your gains stall on a machines-alone approach. Then you have to return to the fundamentals which are...you guessed it, free weights and body weights.
2) Your stabilizers are absofuckinglutely important. The greater the disparity between them and your beach muscles, the higher your risk for injury becomes. And when this happens, you'll lose valuable training time.
3) The most aesthetically pleasing physiques in history primarily used free weights. Do yourself a tremendous favor and look up lifting philosophies from guys like Zane, Nubret, Arnie.
4) The strongest lifters in the past and present primarily use free weights. Sure, they'll employ machines but mostly as accessories.
At the moment, you may only care about how you look, but your priorities may change in the near future.
Talk to any guy or gal who is stronger than they were last month and you'll see an unmistakable fire in their eyes.
Which leads me to this. The best paradigm for LIFE-LONG health is this:
Learn to actually lift free weights with correct form.
Learn and master the basic bodyweight movements such as the pull up, push up, dips, sprinting. No need to learn the super fancy stuff unless you want to explore that realm.
Feel free to incorporate machines AFTER the free weight/body weight movements when the stabilizers have been sufficiently - and hopefully intelligently - worked. This will provide the best of both worlds.