I wrote up a little TS system to test this and make sure I knew what I was talking about.
If it's not currently in a position, it flips a coin and enters randomly at the close of the current bar. I set the SL and TP to be roughly 4*ATR. It won roughly 50% of its trades, as you'd expect. Running on 1 year of H1 bars, it traded about 250 times. WITHOUT any costs or slippage, it generally made somewhere between -$1000 and $1000 (+/- 1000 pips, trading 0.1 lots) in a year. In 10 trials, about 2500 trades, it lost a total of about $1000. Given enough trials I expect it would converge to breakeven.
Then I set the SL to 2*ATR and left the TP at 4*ATR, so the TP was 2*SL. It usually won about 1/3 of its trades, and again it basically broke even before costs.
I ran it on a year of M5 bars, again setting TP/SL at 4*ATR. On the first trial it traded almost 5000 times, won 49.66%, and lost a grand total of $257.23. Setting SL at 2*ATR so PT = 2*SL, it again won about 33% and came out about even.
Then I set TP to 2*SL and got my first surprise. On a year of M5 it traded about 8500 times. Out of 10 trials, 9 were profitable -- not sure why. But even the profitable ones were only averaging about 0.1-0.2 pips per trade, before costs.
So other than that small surprise, this test confirmed what I said -- random entries get you random profits. Costs and slippage will turn that into a guaranteed loser.
Finally, I tried giving it a teensy bit of an edge. Instead of random entries, I tried going long when C > O, when C > C of N bars ago, when C > EMA(C,N), etc. I thought that might be enough to tip the scales to improve it over the random entry, but it didn't help much. The C>EMA(C,N) tests were consistently profitable (except for N in the 250-600 range), but only about 0.1 pips profit per trade. The best result was going long when C > C of 30 bars ago, and even that averaged only 0.50 pips per trade. Those simple tests aren't much better than random entry.