TL;DR - it's not a technical problem but a licensing problem that will solve itself once the contracts expire.
I guess they must be betting that the TV deals will earn them more money in the short term than snubbing them and hoping to build up their audience directly.
But I wonder how many new generation viewers they are losing. Or perhaps major sports was inevitably going to decline anyway compared to alternative entertainment options, so might as well milk the cow while they can.
There's also a ton of added complexity for them aside from the streaming, including having to staff and schedule production facilities for every game. It's not insurmountable, but it's also something they don't deal with today.
If a sports league makes a deal with ESPN and most people get ESPN as part of a bundle, a lot of people are going to watch who might not otherwise watch. If you need to buy NFL-TV to watch a game, many people will simply not watch the game.
Think about how many things that are included with Netflix that you've watched, but you'd never pay for individually. Sports leagues don't want to put people in the situation of deciding if they like the sport enough to pay for it individually. They'd rather have their programming as part of a larger bundle that customers already pay for. Hard-core fans would pay for their sports league, but they'd lose out on all the casual fans, people who might watch a game or two a week (and wouldn't feel like paying for so many games was worth it to them), and people who might watch a game with other people if it was on (and free).