When Coinbase was created/founded, Uber had just launched in Chicago, didn't have UberX and wasn't the brand it is today. Looking at Google Trends data (https://trends.google.com/trends/explore?date=all&q=Uber), the peaks of interest happened in 2016 and in 2019.
So no, the goal of Coinbase before/at launch was unlikely to have been "The Uber of Crypto".
That poem was published between Coinbase's B and C rounds. By that point Uber had done a series E with a post-money valuation north of $40 billion. If Coinbase wasn't looking at that with envy and trying at points to cast their story in the Uber mold for investors, I'd be amazed, because most other startups of the time were.
So no, the goal of Coinbase before/at launch was unlikely to have been "The Uber of Crypto".