Scaling is the delta T transformation of a team or startup from X to X + Y. That transformation can encompass different changes - in people, processes, culture, valuation and almost anything else. I will only talk about startups in the following study.
There are different paths to scaling. Given any amount of time Y, some startups have a greater delta and some smaller. What I mean specifically is that the ratio delta T/Y is greater for some startups, and less for others.
Investors generally like startups with a higher delta T/Y. That means that their capital is being allocated efficiently in a high growth startup, with all else being equal.
The expectations of high delta T/Y probably doesn't vary much between early stage or later stage investors, but logically it should since earlier risk should equal higher reward. But early stage investors oftentimes invest not exclusively for return, but other factors, which could explain why the equality in expectations.
But given investor expectations of scaling, should startups scale faster, earlier to meet those expectations? I think the answer is that it depends.
Scaling faster isn't without risks. Scaling early poses fundamental risk to the business and the team. This is like building the Petronas building while the foundation is moving 100 miles per hour; inevitably without going back and revisiting the structure, at some point the whole thing could come crashing down.
The answer that it depends is dependent on the market and the team. If the market is moving fast, then there is a larger probability to scale as fast. If your competitors are raising massive amounts, then you probably should to. If you think your team or you can build a team that can handle it, then you probably should.
All else - probably not a good time to scale fast. This can include if you want to fundamentally revisit the core premise of what you're doing. As much as there may be internal or external pressure to scale, it probably isn't the right or best thing to do per unit of investor capital.
It's important to remember that the ultimate person that can make that decision to scale is the CEO. The CEO has to make the decision based his or her assessment of the market conditions and the team ability. And that decision is always a good decision, if it was considered deeply and acted upon.