When a potential client fills out a contact form on her website, he tends to share more information about himself when compared to initiating contact by email where only the minimum required information tends to be shared. All website forms also automatically captures the clients IP address and is made available to the recipient. With anonymous email like gmail, your IP email can be seen by Google but such information is usually not available to the email address holder if the emails are accessed via webmail.
Many website contact forms are interfaced with software at the recipients end. This software creates contact lists for the recipient and will automatically populate all the various fields in the contact list creating a valuable database of client information for the provider.
When a client uses email, the provider has to do all the work and enter her clients information manually. Some software will not allow information to be entered manually and requires the provider to maintain a secondary client list or database.
And no, providers do not delete your information after the appointment.
This is the 21st century, providers don't do business like they did twenty years ago. Many are young, tech savvy and much smarter than they make themselves out to be.