Subsidizing own postal service would mean paying it with tax dollars. Why would those who never use this service should pay for those who use it more? Besides that (and its my own observation only) I have noticed that subsidies usually distort market and make service/product less sustainable and competitive.
Same reason I'm ok with the government building a road even though I don't personally drive. It's an economic multiplier. It increases opportunity overall by facilitating more transactions than were previously possible, and the net economic growth can flow back to me even though I didn't directly use it.
I'm not universally in favor of subsidies, just in certain specific instances where the economic multiplier is high and a large fraction of the public benefits directly (usually infrastructure).
They absolutely distort the market! That's the point if you're a government trying to affect your economy. The idea is that everyone collectively paying $X for cheap shipping to be available creates more than $X in economic value.
Someone who doesn't actually take advantage of the cheap shipping directly is 100% benefiting from the businesses they frequent that do.
An argument that might be more familiar in our industry: Why do we spend 10M on advertising when we could use that money to make our product cheaper? Because that 10M spent brings in 12M in revenue.