Oh please, talk about a disingenuous argument. Nobody in their right mind buys paper tickets. Especially as they're priced high to discourage you. That was your choice.
I live in Hammersmith (at the Chiskwick end)... I mostly walk, or sometimes take the bus. Going from Hammersmith Broadway as you were to Shebu is an even shorter walk - probably 10-15 minutes (or the time it took you to buy your tickets, wait for the next train, travel there, and then walk from Goldhawk Rd or Shepherd's Bush Market. If you were going to a concert at the Empire, you only needed to go one stop on the Tube.
If you were going to be driving to Hammersmith, why not just go a bit further and look for free parking on a side street near Shebu? As somebody who lived five minutes walk from the Green, that's what I would do, and what my parents would do when they came to visit me.
BTW, Shepherd's Bush is in Hammersmith, but assuming you were only coming from Hammersmith Broadway (the start of your Tube journey), Shebu is 0.8 miles, much less than your 2 mile business. Yes, that makes it sound more expensive, but also really makes one scratch their head as to your motivation for taking the tube in the first place.