Not really. That used to be possible but there are now so many people doing it that there aren't sufficient arbitrage opportunities to make enough money to cover your costs.
Instead it's more like this:
Consider a hypothetical stock that is worth exactly $1.
What used to happen was that the market makers would have a bid/ask of 0.95/1.05. (For a modern market that still trades with those sorts of spreads, look at gold metal. For small investors, a 5-10% bid/ask spread is fairly typical)
Someone came along and said, hey, I can make money even if I under cut the banks on both sides. So they started offering 0.96/1.04, another competitor, 0.97/1.03 until eventually you end up at 1.00/1.01.
Of course, in real life it's not quite that simple, the price actually moves. While the banks were offering 0.95/1.05, excepting exceptional circumstances, they don't need to update their prices all that often in order to avoid losing money. Of course, they do want to update their prices but it's a fairly leisurely process.
HFT traders can keep their spreads so low because they update their bid/ask prices constantly.
They make money, not by having a big margin, but by having tiny margins but capturing a lot of trade by having the best price. HFT has taken money from the banks and given it back to the investor.. The banks hate it and would love to see it stopped.
That said, there are things that (some) HFT firms are allegedly doing that aren't ideal. One of the things is to enter a new bid/ask into the order book and then cancel it again so quickly that nobody else can take advantage of it.
For example, current market 0.99/1.01. HFT puts in a 1.00 bid and then instantly cancels it again. People see that 1.00 order and try to move towards it - for example the person with the 1.01 ask might cancel it and enter a 1.00 ask instead to try and match the 1.00 only to find it's been cancelled in the 50us it took to react to it. The 1.00 ask now gets cancelled again but the HFT has now entered a 1.01 ask and is now front of the order book.
I have no idea how prevalent this is but if it is, it's easily preventable (orders have to be good in the market for a minimum (short) length of time before they can be cancelled) without having to lose all that is good in HFT.