A cottage economy isn't any worse for your tech rate (better if Financial) and will pick up steam on its own accord.
The big draw with farms + specialists lies in flexibility.
- early Great People. On high levels, the AIs are likelely to run away. A judicious bulb or two can translate into many techs from trading rather than being left in the dust. If you're doing just fine, you can settle them/turn them ito speciality buildings.
- Slavery. Football fields full of cottages produce nothing for a long long time. Football fields full of farms ar reasonable production cities if you need them to be. This means easier expansion, better infrastructure and faster military buildup if you need it.
- An easy way to combat unhappiness. Since you don't rely on commerce, you can turn up the culture slider and wage lengthy wars with far less strain on your economy.