Before app stores existed, smartphones weren't used the way they are today. Consumer habits have shifted... you'd be missing out on a HUGE part of the market.
Missing out on a huge part of the market is comfortable territory for Tumblr
That simply doesn't matter. Tumblr just needs to succeed in ANY slice of the market it can find. A small slice would do nicely.
The best bet would be the slice it originally appealed to, with its original kinds of content, in the original medium it was in.