Or any other alt coin for that matter? I'm wondering if and how it would damage/tarnish Bitcoin's reputation as the Gold standard of all cryptos. I believe it may also affect how institutions view bitcoin, and it may even affect the idea of digital scarcity. No longer can we assume that bitcoin (or its usurper) will remain #1 forever, so how can you imagine it as a safe long term store of value or preserver of wealth? Is the idea of true digital scarcity threatened if bitcoin loses it's #1 rank?
For example, I imagine it would be like silver flipping gold's market cap, (which is practically unthinkable) however, this event would forever alter how gold is perceived, especially by new potential investors.
There was a time years ago in which ethereum was very close to achieve this and there was a difference of only a few billion dollars between the market cap of bitcoin and ethereum, so the scenario that you are presenting had a chance of happening back then, however now the difference between bitcoin and ethereum is so massive that I find it difficult to believe we are ever getting that close to that happening again, since the position of bitcoin not only as the most dominant coin of this market but as a store of value seems to be secure for the long term thanks to institutional investors.
There are really chances to happen in the future as we all know how potential ethereum too as an investment. But that won't trigger bitcoin lovers as bitcoin will always be the highest store of value and the king of crypto market. Big institutions are always looking forward for huge returns so in that case, bitcoin will still be their priority. However, if this will happen in the future, i don't think it will always overtake bitcoin's market cap, maybe for temporary reasons it will.