We use the described setup at our company and the VPN software (Viscosity) auto connects so seamlessly that you never really need to do anything manually. Works really well.
Basically every big corp uses always on VPNs and it works fine. You can even do stuff over group policy on Windows to get the VPN configured and auto join enabled.
Would you care to elaborate? I worked pretty closely with the Corporate IT folks at that company for 6 years and never heard of any issues from them nor complaints from non-tech users in the organization. This company had over 15,000 employees, not the largest but not small.