I'm also not so sure that biting the bullet of a cheap date is as trivial at it seems. I guess it depends on what you're after. But long term, I think you're just delaying the eventual awkwardness that will follow suit if you're planning to do more things together.
The "danger" is that the first couple of times you meet each other sets the initial frame of your relationship, which is virtually impossible to break out from once established. She'll kind put you into a mental category of provider guy.
Say you pay the $20 date, but then she comes to expect the $40 date, then the $100 date, and then if you go on like this she'll expect you to pay for her flight tickets and hotels for vacations and down the road you'll be paying for everything. Not saying it's wrong to be a provider, but IMO then she had to be submissive as hell.
So the low investment might turn big unless you taper down your investment the more sex you have. But it's really a bad strategy. Women will feel a bit cheated and resentful when you change your behaviour in an unfavourable direction after getting sex or commitment.
Better to gradually increase investment instead of the other way around.
In any case there isn't a right answer as to whether you want to pay for everything or split 50/50, but what's important is that you establish a frame that you want, and avoid paying things out of awkwardness or a sense of obligation. Only invite and pay for a dinner you gain a pure sense of pleasure from giving. If you pay for dinners because you have to bite the bullet to follow the script and get sex, then it's not helping you, it's actually harming you in terms of raw sexual attraction. Like
@Chase pointed out, women's genuine sexual attraction toward guys has more to do with frame control than swiping credit cards.
From my experience, women gain attraction points toward me
despite acts of kindness lol. Counter-intuitively, the "worse" you treat a woman the more she'll desire you, atleast sexually.
Mr Variety