Sure, but you do have market players submitting orders based on technical levels which can be found on a chart.
For example today's current Low of Day on ES which was yesterday's closing price. Also known as a gap fill. These levels clearly matter and it's typical with orders clustered around these levels.
There was a poster on this board, NoDoji, who did exactly that, i.e., back-tested chart patterns manually and logged the data. It's perfectly possible.
I've done it myself in the past.
I bet most discretionary traders don't bother to do that, though, and mostly "trade" blindly on what they've read and believe to be true.
As you mention statistical patterns you acknowledge that patterns do exist. These can (but certainly don't need to) be based on data/patterns found on charts as well. I don't see why a pure chartist can not be able to identify and exploit such patterns with a certain degree of success. Those who are good with pattern recognition I'm sure can learn it by osmosis as well if they have enough experience.