So with that said, why use Heroku when you can use AppFog FortRabbit or, dare I say, shared hosting for cheaper and with the same amount of convenience?
Don't get me wrong, the fact that they're supporting these stacks for PHP is cool and I'm one of the minority that doesn't think PHP is going anywhere soon. I'm sure it's a pretty great learning experience for some people to deploy their PHP app on a service like Heroku - there's no doubt about the value in that. I just wonder "why support PHP on Heroku"? I mean, if Heroku one day made it impossible to run PHP apps I don't think many would miss it and may make things easier on the Heroku guys. There's no shortage of platforms that support PHP out there.
I'm also not sure about "PHP isn't going anywhere" being a minority opinion. Even people who disparage it usually understand that its ubiquity, ease of deployment, low learning curve, etc. mean it's unlikely to leave us alone any time soon, if ever.
I don't blame Heroku for this, since they don't officially support PHP, but it was a PITA. Luckily, someone else had already encountered these issues, and I was able to plunk in some pre-built libs.
I chose Heroku because I wanted to familiarize myself with the top PaaS provider, but if I had to do it again, I would have bitten the bullet, learned a new language, and not mentioned it to the client. Or, if I were forced to use PHP, I'd have gone with a provider where it's a first-class citizen.
I am not sure what "Heroku on your local machine" means...
I have a custom php buildpack that I made (forked from heroku, borrowed some other ideas...) but to run it locally I just use PHP-FPM and there's nothing more to it...
I use the wordpress-heroku project  and it has been great.
1 - https://github.com/mhoofman/wordpress-heroku