Another problem with Klobuchar I forgot to mention: her position on internet censorship will probably be unpopular with the base.
Right, but there are also many many Democratic primary voters who don't care a lick about issues like that. Many of whom are the type who voted for Hillary Clinton in 2008, and almost won her the nomination.
Sure, Gillibrand would probably be the stronger candidate of the two, if they were to both run. But we probably won't see both of them running, and Klobuchar's probably the more likely of the two to run. Neither will run if HRC does, and if HRC doesn't run, Klobuchar is still maybe only ~50/50 to run, with Gillibrand less than that. The question for Gillibrand is, does she run if Cuomo does? It would be highly unusual for the junior senator in a state to run for president against the incumbent governor, when the incumbent governor has effective control of the state's political machine and fundraising base. And Gillibrand's young, so she might see it as less risky to wait until 2020 or 2024.
OTOH, if it really looks like no other women are going to run, then Gillibrand might see her opening as "heir to the Hillary Clinton mantle". She would try to build a national fundraising base based on that, and rely less on New York. I'll grant that both Cuomo and Gillibrand running in the same primary strikes me as more plausible than both Bush and Rubio running or both Ryan and Walker running.