I dont think vmware will be phasing out the vsphere client anytime soon... maybe 1 or 2 years down the line it may be replaced completely by the web client.
Also there is no client component to be installed for the web client. Your browser would serve as the client... if you have the appliance, the web client(server) comes bundled with this, so you can point your browser to https://<applianceIP>:9443 and access the web client.
Regards
Girish