Email alias indeed helps to avoid spam and helps you to assume separate identity per site, but won’t help in any way to stop mail provider/server from processing your email data for user profiling / targeted ad purpose.
Buying email domain and self-hosting is only the full proof way from privacy POV, but it is really difficult target to accomplish. A privacy respecting email hosting + alias should be next ideal choice, IMO.
Ah! I was not aware of the fact that Alias service can encrypt email before forwarding to actual mailbox.