Why do people advise diversifying my investments less on different platforms when the capital that I'm starting out with (eg. $5k) to invest is small?

The costs of the different platforms will come into play. The gross returns could be similar but the actual returns could differ as well due to cost.

You could work out the cost of investing for each of your portfolio. And model the cost of each if you only had one portfolio.

The costs will eat into the returns over time.

The rationale behind diversification is risk management/risk reduction. Diversification in your portfolio means you limit exposure to any one market, thereby limiting the potential downside in the event of extended underperformance by that market.

If you buy apples only and apples tank tomorrow, you gg. If you buy 10 fruits, one of which is apples and apples tank tomorrow - you're relatively safe still.

If you invest with Syfe, StashAway and DBS, make sure that the underlying holdings are different. If Syfe helps you buy apples, DBS helps you buy apples, et cetera - in the end all you have are apples.

Also, what Zhe Liang mentioned about platform-specific risk is very important.