We have this exact type of loan on all of our properties, our local bank calls it a "blanket loan". It has worked out really well for us, however we have run into pro's and cons.
Cons: Refinancing every 3 - 5 years. Our bank requires that we refinance the entire portfolio every 3 - 5 years (our choice). This can work in your favor when the rates go down, and it can work against you when rates go up.
Pro's: Its way more of the wild west than a traditional loan, many of the standard rules like 20% down payment's don't apply. We can also really easily play around with equity, as a couple examples. If we want to purchase a new property, we can go to the banker and say: hey we like property X, our blanket loan is currently only at 45% Loan to Value, can we buy this new property with no money down and just roll it into our blanket loan (banker says sure). Same goes when selling, we are selling a property right now that had 75k left on the mortgage - we asked banker if we could just have all of the sale price instead of paying off the 75k, banker says sure you LTV is currently at X% so were ok with that.
There are also some small pros in terms of accounting and easily tracking loan expenses, but to me the main value with this type of loan is the flexibility it offers us, it seems very dependent upon the bank and the individual banker you end up working with - these commercial bankers have a lot of leeway and description it seems like.
hope that info is helpful!