Again, not necessarily. HZ is a toolkit, and a low token price helps to issue assets or currencies and send them around, or cast votes. Assets and coins don't need to be tradable, for coins it's even possible to disallow it.
The only one who needs a high price and liquidity is someone who wants to sell a bunch, for example crowdfunders.
Yes, that's right. A low price is no deterrent at all to many projects: crowdfunding is one of the few.