Except... reality is harsh and ugly.
You want the guy with the sysadmin foo on your team from as early as possible. Because if your thinking goes along the lines you just described then clearly you don't have him yet, nor someone who told you what slippery slope you're about to tie yourself to.
If you have the admin guy then he will find you a cost effective platform to start out with quite effortlessly. Which might be heroku in some cases, but is usually just a bunch of rented or virtual servers that he sets up over a weekend. In the latter case it might actually cost a few bucks more initially than the "heroku free plan" - but he'll explain to you in kind words why he thinks it's worth that in the midterm. And he'll probably be right.
If you don't have him, then heroku can't save you. Heroku will run your stuff for a while just until things get interesting and worthwhile load starts to build. That's the point where the sum of your mistakes brings it to its knees. Due to basic mistakes usually. Related to simple things like file descriptor limits, stuff about TCP connections, or a basic understanding of how disk i/o works and how to craft the SQL to make it not hurt so much.
At that point all you can hope for is that you're already profitable enough to afford not only that guy you skipped on initially, but rather his bigger, hairy brother, which is the only kind generally willing [and able] to take on "search & rescue" gigs. For an adequate sum.
At this point your friendly "pay-later" route has turned into a nasty "pay 10-20x now" roadblock. In an "Insert coin to continue" sort of way.
This is not about what heroku can or can not do. This is about what kind of skills you need on the team for a web-startup. Don't skip on the admin. Or rather, don't skip on at least one guy who has been doing the admin thing on a real live app for a bit and also during some not-so-good times.