What about Yodlee? I'm under the impression that Yodlee is a bigger and much more established player here. Although Yodlee's API certainly isn't great.
I developed both Yodlee and Plaid integrations for a customer last year. I remember the Yodlee sales rep mentioning that over 75% of their supported institutions are direct API integrations. Now, this is coming from a sales rep so take it with a grain of salt.