Does the MVC framework, whether it be ASP.NET or Rails enforce you to develop better databases?
Since your database tables and fields will most likely map to classes and properties using OR/M, it only makes sense that this would force you to create a proper database structure from the beginning of development.
You underestimate the ability of people if you think any set of rules can successfully force someone to perform better.
MVC framework is very much a "Model" centric architecture and it only allows you ti interact with your database in an efficient way, id does not force you to design a database in a particular way
Physical data layer may be different (and usually is) from the entity model that's usually used by EF/NHib/likes.
But whenever you do any kind of abstraction of your data model to your code you do tend to change certain parts. These adaptations relate to flexibility of your OR/M. The more flexible it is less adaptations there will be.
I don't think it does.
MVC does not have anything to do with the database design, it is more towards proper architecture.
But it may indirectly improve the database design by introducing the use of model or domain driven design.
As it's entirely possible to create an application using the MVC pattern that doesn't use a database at all, then the answer is no. I don't think the original implementation of MVC in Smalltalk-80 (as in 1980) was RDBMS-backed.