Some important points about VLT Peer routing technology.

Peer routing enables one VLT node to act as a proxy gateway for the other peer in a VLT domain. When you enable routing on VLT peers,
you can also enable the peer routing feature.  

In a nutshell, when peer-routing is enabled on both VLT switches you can load-balance, the L3 packets through both switches – as this allows a switch in VLT domain to forward traffic on behalf of its peer switch.

Example how VLT forwards the traffic without peer-routing enabled :

 

When you enable peer-routing :

Images taken from Configuration guide

Peer-routing helps to avoid sub-optimal routing, reduces the latency by avoiding another hop in traffic path, no need to have VRRP.

Keep in mind in case if switch – Peer-1 will fail with peer routing enabled, your traffic will still be forwarded without any interruption – but as you don’t have any virtual IP address any control or management plane requests won’t be answered by Switch-1’s peer.

So basically by enabling peer routing we have only one goal – redundancy and traffic sharing for L3 protocols.

During the bootup of VLT peer switches, a forwarding loop may occur until the VLT confgurations are applied on each switch and the
primary/secondary roles are determined.

To prevent the interfaces in the VLT interconnect trunk and RSTP-enabled VLT ports from entering a Forwarding state and creating a
traffic loop in a VLT domain, take the following steps.

1 Configure RSTP in the core network and on each peer switch as described in Rapid Spanning Tree Protocol (RSTP).
Disabling RSTP on one VLT peer may result in a VLT domain failure.

2 Enable RSTP on each peer switch.
PROTOCOL SPANNING TREE RSTP mode
no disable

3 Configure each peer switch with a unique bridge priority.
PROTOCOL SPANNING TREE RSTP mode
bridge-priority

More info about peer-routing advantages comparing to VRRP.

https://hasanmansur.com/2016/06/09/vlt-peer-routing-and-routed-vlt/

Routed VLT v1.2 – document covers peer-routing in great details.