I think we are missing his “wisdom”. If we had his wisdom we would know the answer for certain. But I will share what I hope are two “wise” approaches to answer your question.
1. Perhaps the premise of your question is incorrect. Maybe it would be wiser to be without cars. There are “natural” modes of transportation that are fast, reliable and safer. A famous Rabbi of the previous generation stated that if he had the authority he would ban the use of cars altogether for safety reasons.
Our Sages teach, "Who is wise? One who sees the outcome." We often don't see the total outcome of our actions until we gain the perspective of time, if at all. Is it always truly clear what is "wise" or not?
Accordingly, King Solomon used his wisdom to choose what to do and what not. What to make and what not. I am not wise enough to understand all the “calculations” that went into making a decision, but we often have a glimpse of the pros and cons of new inventions in the world. I am a nuclear scientist (as well as a rabbi) and I doubt if I am alone in feeling more than “uncomfortable” with the threat of a possible nuclear war, God forbid.
2. Another approach to why King Solomon did not invent advanced technology in his time is that he lacked the infrastructure. King Solomon lived before the “Industrial Revolution” and lacked the tools, materials and processes for inventing a car and other inventions. Although he could have invented the lacking technology if he wanted, it would have been seen as miraculous at the time, and he felt it wiser to live according to the norms and means of his day.