There's a lot to add to this article in my opinion:

Many lenders refinance loans because lenders also need to finance their activities and refinancing through securitization is a profitable way to do so, that goes for student loans, business loans, private loans, car loans, ...

Mortgages are no exception, what is different about the US compared to Europe is that the capital market to buy packages of loans is more developed because unlike the EU, the US is a unified financial and legal system under federal governance.

What happens in a mortgage is not that much different than a car loan, you use some cash and borrowed money to pay for the car and the lender expects you to repay that money (and interest) in fixed installments. Should you fail to pay the loan then the car is repossessed.
The lender will want to make sure that your monthly salary is enough to cover the payments and that the car is valuable enough to recover the principle of the loan should something happen.

Incidentally, this is why banks don't like to give entrepreneurs mortgages because entrepreneurs don't have stable income (usually).

The moment you borrow that money, it becomes a liability for you but it becomes an asset for the bank/originator; after all you are going to pay the originator cash for 25 years.

Now in the US, your originator can sell this asset onwards to a loan aggregator (Fannie Mae; Freddie Mac) to realize profits today rather than hold the mortgage forever but obviously the loan aggregator has some standards it wants you to adhere too. (note: the EU doesn't have these types of loan aggregators due to the lack of synchronization between their national financial markets)

In theory the originator can make more profit by holding the mortgage, but since his money is locked up for 30 years in the mortgage; many of them don't have enough cash on hand to just lend the money and wait 30 years for it to come back so it can be lended out again.

The loan aggregators on the other hand buy mortgages from all originators and can put them together into a package that is safe and diversified enough so that the repayment performance is predictable enough (ignoring pre-2007 when rating agencies succumbed to customers' pressure to rate pretty much anything as safe and caused the huge financial meltdown when borrowers started to predictably default) and sell it onward to pension and sovereign wealth funds.

These aggregators, or GSEs as patio11 calls them, are private companies but by now they are government owned because they all collapsed in the financial crisis and since they underwrite pretty much every mortgage in the US, they had to be saved as otherwise the mortgage originators would also become illiquid and then you can only buy a house in cash (which would have pretty much destroyed the entire housing market in 2008).

The 60 basispoints though, is the fee for packaging the loans. It's not an insurance like patio11 says.

Operational work like support, collections, negotiations about late payment and administrative work ("Servicing") is outsourced is just because no loan aggregator wants to deal with that and a pension fund DEFINITELY doesn't want to deal with that and like any outsourced service that is well-understood, they prefer to pay as little as possible for this part. This creates natural market pressure for consolidation.