One can make a case for both design alternatives. Which is best for your environment really depends on an assessment based on the criteria and requirements you have.
Even as an engineer who primarily works with security products I realize that they are not always the right tool for the job. Firewalls route with much less capability than routers (and even than many switches with routing enabled). Routers and switches generally don't do IPS and file inspection and such. So there is a place for that in the firewall. There is also a lot of host layer security that can be implemented so that is yet another consideration.
If I had to make a snap decision, I would say that "firewall everywhere" is not the best choice. It can work in in some environments but generally does not scale well (unless you pour a lot of money into the solution).
