There is likely not enough Market Depth, even if the turnover is high.
Market depth is the market's ability to sustain relatively large market orders without impacting the price of the security
https://www.investopedia.com/terms/m/marketdepth.asp
Always remember that to buy a share you need to find someone who is willing to sell it to you. Say the company has 99,999 shares issues and a current trading price of $1; you might be able to buy the first 49,999 for 1$ each*, but the current shareholder(s) know that selling you that last share gives you control of the company. If they don't want that, then that last share may become very expensive indeed!
*In reality if you start to buy large volumes of anything you'll move the price, but let's keep the example simple.
EDIT: Let's also think about how much the price might move even without the risk of you owning more than half:
Start price = S0 = 1$
Increase = r = 0.01% per share bought (that's not a lot right?)
Shares to buy = N = 50,000
Final share price = S0 * r^N = 1 * (1.0001)^50000 = 150 $
Total spent = S_0 * (1-r^N)/(1-r) = 1 * (1-1.0001^50000)/(1-1.0001) = 1.47 $m
Set the rate a bit higher:
Increase = 0.02% per share
Total = 110$m !!
That doesn't look so cheap any more!