IIRC, the rule was established because some bad monks, used vehicle pulled by animal or (female) slaves.
This was criticized, because that is the behavior of the rich, also it exploits other living beings.
At that time the monks from the group of six traveled in vehicles, sometimes pulled by a female animal with a man driving, at other times pulled by a male animal with a woman driving. People complained and criticized them, “It’s as if they’re at the Ganges festival.” They told the Buddha.
“You should not travel in a vehicle. If you do, you commit an offense of wrong conduct.”
The group of six, is the infamous group of bad monks who caused all sort of rules to be established.
Based on the origin of the rule, vehicle can be used if it is not unreasonably luxurious, and not exploiting other living beings. The rule already has precedent of being relaxed.
Soon afterwards a monk who was traveling through the Kosalan country on his way to visit the Buddha at Sāvatthī became sick. He stepped off the path and sat down at the foot of a tree. People saw him and said to him, “Venerable, where are you going?”
“I’m going to Sāvatthī to visit the Buddha.”
“Please come with us.”
“I can’t. I’m sick.”
“Then please come inside the vehicle.”
“Thank you, but the Buddha has prohibited us from traveling in vehicles.” Because he was afraid of wrongdoing, he did not accept. When he arrived at Sāvatthī, he told the monks what had happened. They in turn told the Buddha, who said,
“I allow a vehicle when you’re sick.”
The monks thought, “Pulled by a female or by a male?”
“I allow a rickshaw pulled by men.”
Soon afterwards a certain monk was even more uncomfortable when jolted around in a vehicle.
“I allow a palanquin and a litter.”
https://suttacentral.net/pli-tv-kd5/en/brahmali?layout=plain&reference=none¬es=none&highlight=false&script=latin