The main driver of consultancy is revenue. If you can survive without that, don't do it if it isn't core to your business, just like you wouldn't do in an established company anyway.
I've worked at a startup which, bootstrapped, was struggling with income flow. So off-and-on we, the programmers, would be outsourced to gigs that would generate some income. I've always found this the worst of all options and decided to never get into this with my own startup.
It takes away the most valuable resources. It's a negative investment. It advertises the "panic-mode" you are in, to all stakeholders and most to the engineers involved. It lands your engineers (me, in that case) in crappy jobs, which they did not sign up to at all (a few engineers left because of this). It creates misaligned relations in the team.
The last was for me the most frustrating. At one point, I was bringing in ~60% of all revenue, alone, by doing crap work, in stressfull projects, and commuting for hours a day. While at least two of my co-workers, whose wages I was subsidising, turned up at 11:30 to drink coffee and play some FIFA on the company x-box.
What I learned from this, is that hiring too early is a thing too. That, especially when bootstrapping, the income stream must be certain enough to warrant paying another wage for years.
From your example the consultancy work wasn't the problem, it was mismanagement of the of the startup.
The only alternative to consultancy should be to close. If you can let go of 1-2 unproductive employees, that should happen before taking on consultancy work. It should happen in any circumstance anyway, but taking on work to pay for other peoples wage and not getting value for that is a recipe for failure. If on the other hand it was high performance developers that really made progress on the core focus on the business it's probably okay.
