You certainly could use a L2 switch, and it would probably work just fine. But here are a few reasons why a L3 switch might be a better choice:
You may want to segregate your servers into different VLANs to
simplify access control, apply QoS, limit failure domains, etc. An L3
switch will make this much easier.
While Firewalls can run routing protocols, they don't seem to do it
as well as routers, except in the most simplest of cases.
Network management features are usually more mature on routers than
In many organizations, firewalls are administered by the security
team (a bad idea, IMO), so they need to get involved if routing
changes are needed. It's better if network routing is controlled by
a single administrative group.
In the simple diagram you presented, there aren't many routing decisions to be made (there is only one data path), so static routes would probably suffice. but if you start adding redundant switches with redundant paths, then you need devices that can detect and respond to topology changes -- i.e. run routing protocols. "Daisy-chaining" routers is not going to cause problems unless the network is very large.