Pretty good question! Goes way beyond the scholarship.
I know a number of folks who subscribe to your theory (they are sitting on big chunks of cash and hating the DOW hitting 29K). I talked to a financial advisor and they told me to hold back some cash too - it seems everyone is holding back the cash, which I feel this next recession will be different because so many people are expecting things to hit the fan and so many are holding back the cash. A couple of my friends and I pulled money out of stock market back in 2018 when it was 24,000. Was not so smart

Some are still waiting to get back in.
And the interest rates are so low still so it is easy to borrow to have cash on your hands. I wonder if that will be the downfall - too many people holding out and then giving up and plunging (that's kind of what happened in the dot.com bust when peole could not believe stock could grow so high and it still kept growing so fear of missing out set in).
In terms of your situation, do you have access to other sources of funding if you need emergency funds? E.g. can you get an easy personal loan without paying 19% to credit cards? I would make sure you don't surrender all of your cash and you have an emergency fund. Your loan does not sound significant enough to make a big difference in the grand scheme of things since it likely will take years for it to double. Last time around it took 5-6 years for the stock market to double and while that's impressive that would trigger 5-6 years of moderate interest you would be paying on your student loan. I think it would be somewhat muted result, and would only play out if the investment returns are sudden and fast which is not possible to count on...
Bottom line: I would borrow if your emergency fund is compromised or low. I would borrow if I were into finance and loved investing and developing a strategy then sure but normally I would not recommend it just to have cash in case the market drops. Lots of other people do and they won't let the investments go super low with their deep pockets.
Disclaimer: don't listen to my financial advice - I usually get it completely wrong

P.S. The super weird part is that the most growth seems to have occured between 2016 and 2018 and then the difficulty of timing the market... it will be hard to pull off but it could be fun if you can borrow cheaply.