They did that in the old days, before 1984 I think. Drivers would simply 'ride the arm', that is not turn on the meter for long rides, like the airport etc. So they even put in a device in the seats that automatically turned on the meter after a set time. I remember I saw my dad driving, and tried to sit so that the meter wouldn't turn on- no luck.
In reality, you should be able to get more than 50% of the take. Some nights it could be as high as 70%. The main thing is that you should realize that you need to make TIME not MONEY. Making time, like taking toll routes even if you have to pay for it yourself, will allow you to make more money later on. Taking local streets during rush hour might be better than highways, and going 'off duty' when heading westbound or eastbound during rush hour lowers your chance of getting stuck in crosstown traffic. I can never figure out why drivers would willingly go over the Brooklyn in rush hour traffic, even if the passenger says no to the toll. If they say no to the toll, then offer to pay it for them- like 99% of the time they accept. So you are out like $5, but you just MADE 30 minutes, which should be around $20 in rush hour traffic. You have a net increase of $15, well worth your investment in the toll. And here is a secret- many times the amount of the trip will be the same as the no-toll way, so often the passenger will offer to pay it, or at least pay half. All, half, or none, you still win. Make TIME, not MONEY!!!
Also, you need to really figure out what the person wants. If they say PATH train, Grand Central, or Penn, I always ask them where they are eventually heading. About 1/3 of the time for PATH, maybe 1/5 of the time for Grand Central and Penn, I can cut them a deal to get to where they want to go- but of course you need to keep an eye on the time. A ride to NJ is great at 12pm at night for both of you, not so great at 5pm, right? They get home quick, you make easy money sailing along the highway at night. So again, make TIME, not MONEY, your major gauge of how you are doing. Because, in reality, if you make enough time, you will have plenty of time to make money.