I built two different consulting groups and both were successful and made good money. One even took a modest outside investment at a point to grow faster, just not VC dollars. You can absolutely scale a consulting business into the billions of dollars of revenue, hello KPMG, IBM Global Services, etc etc.
What makes consulting businesses non-compatible with venture capital is that VC's are looking for leverage on their investment, they don't care about "scaling". Founders get hung up on "scaling" cause it is the term we use when growing the business as a catch all, scale people, sales etc. But financially speaking VC's generally look at leverage on their dollar not scaling, in fact, they want you to stay as small and lean as possible but leveraging their money to make more money while spending the smallest amount reasonable.
I am not trying to be argumentative, and I get the difference is subtle but it is a critical difference. You can research this and you will find they are different. For example, you could scale out your sales and team yet remain unprofitable, which means you didn't leverage the investment very well.
I point this out because if you can show an investor how you can leverage their dollars into more dollars, generally that's how you can get an investment. VC's don't play the game in this way for valid (and sometimes invalid) reasons but high net worth individuals do, and frankly for a consulting business a few HNI's are always a better source of funding.
Venture capital is about scalability (i.e. cost per unit goes down when number of units goes up - preferably considerably...)
Consultancies are unscaleable business by design, because they sell "hours". Every employee can deliver a certain number of hours only, so per-unit (marginal) cost is flat.
And therefore VC and consultancies does not match... at all..