I'm curious what the source of the burn is.
We recently got bit (not quite burned) with the load balancers in the Common Runtime being shared across all apps.
Some piece of malware was associated with one of the IPs of Heroku's load balancers. One of our customers ended up blocking one of our servers associated to that IP because of it. We did some research and we even think we know what app caused it (it's someone's app they host on Heroku), and we don't think it should be flagged as malware, but either way... some other app in Heroku could be truly doing bad things and we would then get our server blocked again.
Heroku's advice was to put up a CDN in front of their load balancers, which has worked for now. But that's extra cost and system complexity just to get around a limitation of Heroku.
We did confirm a Heroku Private Space would eliminate this, since we'd get our own set of IPs for the Private Space's load balancers. But that comes with extra cost, and perhaps even limiting which add-ons we can use in the Private Space.
So although we've generally been happy with Heroku, we are concerned with some technical limitations, like this important (to us) one.