Competitive players like Carlos Alcaraz don't want to lose a single match, let alone one which can be considered one of the biggest upsets in recent memory. It wasn't a particularly great match from Alcaraz as he was rather sluggish compared to his bouncy self.
Fatigue is a likely cause despite him vehemently denying that but in the end, the result was the same. He packed his bags and flew back home to Spain. The result itself could actually prove a blessing in disguise for the Spaniard so let's break it down.
The main concern in his relatively young career so far have been injuries. Being as self-aware as he is, means that he understands that too and he actually named injuries as one of the rare things that could stop him in the future.
Injuries are bad luck most of the time but being fatigued certainly increases the risk for injuries and more broadly, Alcaraz himself hasn't done that well when playing consecutive weeks.
He opted to play on short rest after his US Open triumph by taking part in the Davis Cup but he didn't play well. He didn't play well at the next event either so it took him some time to properly recover. Playing two 10+ day events back to back and going deep would have likely done more harm than good to Alcaraz.
Especially with Roland Garros so close. The earlier exit from Rome gives him a chance to properly recover for Roland Garros having 10+ days between his last two matches. It's certainly something that he benefited from earlier as well.
Last year's Cincinnati Masters saw him lose in quarter-final giving him over a week to prepare for the US Open. It didn't go that badly for him as he won his maiden Grand Slam trophy at the event.
He's eyeing a second in Paris and he might just be the biggest favourite. Nadal's withdrawal certainly makes him appear so though with that comes more pressure. That is something that proved his undoing at last year's event.