Taxi/Lyft are waaay more expensive than the subway. Unlimited subway/bus is $116.50 per month. Taxi/Lyft could easily be $50/day or more depending on how far out you live. This is not a viable alternative for most people.
But, for the occasional trip the cost benifit tradeoff of the city saving vast mounts of money and reduced delays is worth a few people being inconvenienced.
Ahh, did not realize you where trolling about a world without bridges. I mean wtf dude, the inefficiency from running a 24/7 subway reduces the city's ability to afford more bridges.
Further, Manhattan is just not that big. Nowhere is very far from anywhere else when you step aside from the horrid congestion.
The commuter tax deduction lets you buy the cards with pre-tax money deducted from your paycheck, which is a substantial reduction up to 45% or so depending on your marginal tax rate. Of course, because it's using pre-tax money, it's giving a bigger discount to higher earners, which makes it the opposite of progressive, which seems opposite of what's intended.
Separately, seniors/disabled people pay half fare: http://web.mta.info/nyct/fare/rfindex.htm