self-funding growth from profitability pretty much guarantees you are locked into a relatively slow growth rateThat's an unwarranted assumption. Part of designing a startup business model is organizing growth so that you are unconstrained, so that more input produces greater output, earlier -- whether it's capital, users, employees, or support. All it takes is for one component of your business to not scale and you won't hit your growth numbers despite the brilliance of every other part.
Capital is just one of the areas you have to look at. Amazon is a decent example. Bezos chose books because it was (a) accessible (catalogs existed), and (b) he got 6 months to pay back booksellers, which meant he could afford to grow the more he sold, by using the money owed to the booksellers as float.
Startups would do well to evaluate all possible constraints on growth, capital and otherwise. Many times small tweaks to how you sell your product (or what product you sell) can produce large variations in the amount and timing of capital needed.
Here's an example: do you have customers pay for the first 30 days up front, with an option to cancel within that time? Or do you charge your customers after the first 30 days are up?
Now, you'd think the latter would always be better for "growth", because it involves a weaker commitment -- no money changes hands early.
But it also has a huge capital cost differential, if the service costs a substantial amount of money to deliver. In order to grow the latter model, you'll have to obtain more and more capital over time as you grow.
But if you do the former, you can "fund" your company's growth off of its earlier growth. Although this might impact growth negatively, by turning away customers that "won't pay" for the first 30 days up front, but who would have become customers the other way.
So which is better? It really depends. If your growth rate is already 7% with the pay-up-front model, that's better IMO than getting, say, an 8% growth rate with the pay-after model. The latter will require raising increasingly greater amounts of capital, despite the fact that it's growing "faster" initially, ultimately hurting your growth or wiping out your equity, or both.
Both approaches will still have their "S" curves end up at the same place (the market size doesn't change), but let's be blunt here: no company can catches up to 7% growth, so wasting your equity on 8% growth just makes you poorer, and the VCs richer.
Sustainable growth is just as important, and treating capital as something you "have to" raise is exactly what VCs want you to think, since, hey, that's what they sell. Venture capital is a financial tool, not the only (real) way to capitalize a startup during and after growth.