Why can't I walk up to the stock market and buy a single share of Facebook?
If you have a membership on an exchange, the marginal cost of buying one share of FB would be the liquidity removal fee of $0.0030 (three tenths of a penny)†. But you don't have membership on any exchanges, so you have to buy your share through a third party, a stock broker.
Your broker is providing a service that has costs. Exchange connectivity is not free. Brokerage staff do not work for free. The website and backend technology are not free. Clearing is not free. Those costs have to be passed on.
There is a lot of healthy competition in the retail brokerage space. It's relatively easy to move your holdings from one brokerage to another, which suggests that competition has driven transaction fees to a level that allows brokers to cover their costs and provide a small profit.
Because the stock market is not a store. The price of a share of stock does not include the cost of running the market and its infrastructure.
If you want to invest without fees, find a no-fee mutual fund with low minimum investments. At the scale where $7-10 fees are onerous, I find it highly unlikely you have the money or sophistication to be investing in individual volatile securities.
Why can't I walk up to the stock market and buy a single share of Facebook?