I have a wide ip which has one pool with two LTM VIPs in two different DCs. Load Balancing method on GTM is Round robin and LTM VIP is configured with source persistence of 60 minutes. We have seen lot of issues in past few months, due to which Apps team have disabled one of the DCs. Right now only DC is taking all the traffic which has fixed the issue. I would like to understand why it is a bad design to have Round robin in GTM with LTM persistence on the corresponding VIP
You need to read about F5 LTM and GTM in Learn F5 to get the basics on how it works and it is free.
From what I hear here maybe also application wants the same F5 LTM device and VIP/pool/pool member to be used after the fist time the client logs in as maybe the server saves a client info or the client uses a cookie that the server has provided and this is why the LTM has source persistence (which is something I will only use if cookie or SSL session or Universal persistance are not an option as NAT before the F5 device will cause uneven load balancing but this is another story).
So when the GTM provides another IP address for the dns resolution that is the IP address of another VIP on another LTM device than the one the customer used after the initial login/first request this will lead to another server in the othe DC to be used and it will break the application, for example the shopping cart will be empty but the customer selected things when he did log into for the first time 45 minutes ago.
The GTM/DNS also has persistence so you can test that as a solution or use Global Availability load balancing on the Wide IP and and Wide IP pool.