In my case it came down to $242/mo vs anywhere from $360 to $480/mo with Uber. It's not clear to me that had I invested the purchase price the 7% return would be enough to make up the difference of $120-240/mo. Certainly not in the first year. I'd have to do the math to see when the breakeven point would be where that initial investment is yielding more than the extra cost of using Uber.
There's also the fact that 7% is the market's return, which is over a 30 year span. On a 10 year span, the rate of return is highly volatile, and could even be negative (on the flip side, could be a lot more than 7%).
I just ran the numbers, BTW. With my purchase price, invested at 7%, I break even after 7 years (just about the time I owned it) - assuming Uber is the upper bound of $480/mo. At the $360/mo cost I'd break even after 3-4 years.
I didn't take into account the sale price, so that would make the breakeven point a little farther.
For example, let's say you bought your car for 10k, then sold it 7.1 years later for 9k. You have 1k of depreciation. You also have $6,300 at 7%(a typical target rate) in lost income from not keeping that money in a productive asset for those years.