Who "owns" the customer relationship?

I had an interesting conversation this week with an Account Executive (Sales) at a SaaS company.   We were talking about how, in many companies, the Account Executive "owns" the customer relationship. However, in his current company the post-sale team owns the relationship and it makes his job more challenging with existing customers.  So, the question is, who should "own" the customer relationship in a SaaS company? The answer to this question dictates how the internal processes are executed. Everyone brings different skillsets to the table, and all are needed at different times in the customer's "life" with your company.   Does one particular organization (e.g., Customer Success) need to own the customer relationship or is a different model appropriate in a SaaS company?

First, I am really talking about SaaS companies that have high-touch services that require ongoing involvement of the vendor with the customer. If your company has many customers and the relationship post-sale is low-touch, this probably doesn't apply nearly as much.  In this case the "face" of the company is the indirect interactions such as your email pushes and texts.  It also includes all the interactions where the customer contacts you for things such as customer support, re-orders, etc.   To the extent you can personalize that, the better. So, for example, I interact with a person when I have an issue and I have a phone call or a chat session with the company and I talk with "Joe" or "Mary" from customer support.

In a high-touch SaaS company it is different.  From the customer's point of view, multiple vendor people/functions interact with them and the customer should never have to think about who they are dealing with - Customer Success Manager, Sales Exec, Customer Support.  Each should be handling the need of the customer flawlessly. That should be the goal of a SaaS company, so the question is not what does the customer need;  the question what does the SaaS company need to be most successful.  If the Sales Exec doesn't hear about a potential need in the customer's organization, will an incremental sale be made, or will it be passed up? If the Sales team owns the relationship, will the customer go to them first when they should be going to a Customer Success Manager?

I have some thoughts on this that I will post as a follow up.  What are your thoughts on this? How should the customer relationship be managed in a high-touch, SaaS company? What should the responsibilities be?  What technology can be used as part of the solution?