Can wordpress do this? Should it?

I’m looking to create a Software as a Service and wanted to hear you thoughts on the feasibility of using WordPress as my platform.

There is a small business niche I would like to cater to but the business logic is hard to explain so I’ll use restaurants as my example since that is easily relate-able

I start restaurantwebpage.com where I create some custom plugins catered to the restaurant business.

Owners can sign up on restaurantwebpage.com for a monthly fee and in exchange they get numberonechina.com to create their website. Static pages for their content, a food blog, and a menu creation plugin or something.

#1 China’s customers can in turn sign up, for free of course, on numberonechina.com and create save their favorite meal(s) and place carry out orders. Sign up for a newsletter to get coupons or buy a giftcard or something..

Repeat this for the next restaurantwebpage.com users creating mulligansbar.com, saltynachos.com, etc

Everything runs on the same code base. If this gets big I don’t want to update 100 sites individually. If I add a new custom plugin everyone gets access to use it.

It is not necessary that customers of the individual restaurants can re-use their login info for another restaurant running on my platform

Finally for themes I would like 3 levels:
free- everyone can pick from these
premium- addon to unlock extra themes
custom- a restaurant hires their own web designer and only that place can use this theme

Can wordpress do all of this? I come from a custom php/rails background of building webpages, but always when doing the CMS part, it sucks, and WP seems to excel at that part. So I’m looking to change my perspective: start with a great CMS and addon on the custom bits