Moving to breakeven removes open-trade-risk and frees budget under max-open-risk. That capacity argument is the strongest case for it.
The performance case is weaker than it feels. Moving a stop to entry after +0.5R converts a population of trades that would have dipped and recovered into a population of scratches. If 30% of your eventual +3R winners first retrace below entry-plus-noise, the rule deletes almost a third of your best outcomes to avoid small losses you had already budgeted for. Run the test on your own r-distribution before adopting it; many traders find the rule costs 0.1-0.2R per trade.
It also does not make the trade risk-free. See risk-free-position and gap-risk: a stop at entry is an intention the market honours only when it is open and orderly.
Related: risk-free-position, open-trade-risk, trailing-stop, r-distribution