HSRP is used in the first instance for gateway-redundacy, e.g. in client VLANs.
If you use a routed port, you have to connect a switch to that port to connect the clients.
A c3750 doesn't support routed subinterfaces, so if you need more then 1 VLAN (which is normally the case), you have to use another Uplink for that (instead of simply use a trunk). Even the link to your HSRP standby router can't be the classic interswitch-link between them. Connecitvity ist formed across an access-switch - which is normally not desirable.
In addition, if the client-VLAN ist needed on another switch, you can't use an uplink of your c3570. This is not scalable and doesn't meet common Campus-LAN Design requirements.