Not really. Pricing gets complicated for enterprise sales so it can't be as simple as just signing up online. Furthermore, if it's a trial they are signing up for then they have to be put into the sales funnel (meaning they have to sift through a bunch of tirekickers to find the real buyers). Finally you'd have to worry about fraud, trial abuse and all of the other related pains of free and open signups.
There's a reason that basically every business in the industry does it this way.
There's a reason that basically every business in the industry does it this way.