Shurmur fits the Browns for multiple reasons.
Losing Shurmur would threaten the Rams' continuity unless the team found a replacement to run the same system. Former Minnesota Vikings coach Brad Childress comes to mind. Like Shurmur, Childress has roots in Andy Reid's offense.
Maintaining continuity would help quarterback Sam Bradford. That's why former Denver Broncos coach Josh McDaniels might be a better fit somewhere other than St. Louis if Shurmur does leave the Rams. McDaniels is hoping to reemerge as a head coaching candidate after spending a couple years as a coordinator.
I think the Rams would be best off having the same coordinator, or at least the same system, in place for the long haul.