If I sell sandwiches to 10 people at $10 per sandwich, then raise the price to $30 and lose 5 customers.

[ProfessorGAC]

16. The Ideal Point Is Called Equilibrium

It's the point that maximizes volume at which the entire supply will be sold at a price point that maximizes margins.
Your thought that just raising prices doesn't work in reality when the price gets prohibitive. There's a upper limit.
In your example, losing 50% of customers at 3x the price is awfully optimistic.
That approach might work if there were nobody out there to compete on price.
Profits go up whether it's because unit price increases or volume goes up. Increased volumes often are ideal because few businesses are constantly running at 100% capacity. So, increased volume carries no added overhead, only raw materuak costs.
If demand gets to the point where added expense, or capital, or both are needed the value of growth vs. short term profits becomes part of the decision making process.
Be careful not to get caught in the Econ 101 trap that supply & demand functions as 2 dimensional, X therefore Y, constructs.
In reality, there are several X's exerting leverage on the outcomes.