Well 1st. Market Cap is actually meaningless without looking at Profits and Revenue. Intel is ridiculously profitable. If Intel were rated with the same P/E as TSMC Intel would more than double its current market cap.
2nd Is the conflict of Interest. The reason why people trust TSMC is because TSMC do not compete with them. TSMC do not sell CPU / GPU/ I/O Controller/ Network Controller / FPGA / SSD Controller / Modem / Embedded SoC etc....
Intel does all of the above. i.e Why would Nvidia or AMD Fab with Intel to compete with their own CPU and GPU?
3rd, Fabs requires economy of scale, the key reason why TSMC managed to catch up to Intel is the sheer volume driven by the Smartphone revolution. Unless Intel decide to drop their product business they will never be able to achieve that scale.
4th is as mentioned in the post above, culture.
There are few other smaller points, but these four are big items that cant easily be changed.
1. Market cap factors in profit, revenue, potential growth, opportunities, and basically everything about the company. It's a better measurement than just profit and revenue. It's the single most important way to value a company because... it's the value of a company. It's why wildly profitable companies are often worth way less than a loss-making high growth company. Uber is an example.
2. The same reason sellers sell on Amazin despite Amazon selling their own brand of items. When your technology is so much better than the competition, customers don't have a choice. This was the case with Intel's process lead before TSMC and Samsung took the lead. In addition, Intel could have spun off the manufacturing business as a separate entity to reduce conflict of interest.
3. Intel had more scale than TSMC before the smartphone revolution. They just didn't see the opportunity.
4. I'd argue that it's not culture. It's the lack of business leadership. I'm sure Intel had internal discussions of creating manufacturing as a service business but they didn't take it seriously enough.
The point is that Intel had a great opportunity to own TSMC's business. They didn't execute on it.