a BETTER coin, one with improved technology can replace bitcoin .... the improvement must be very significant and bitcoin needs to stagnate and fail to improve over a very long time....
If a coin can be replaced over night by another coin with better technology ...nobody is going to want to hold any significant value in any coins....People will stop buying them. If there's not faith in a currency staying around and holding value it won't hold any value at all.
You really need to distinguish a variety of cases and phases of development in order to apply that reasoning suitably.
Firstly, we should distinguish application tokens and financial engineering vehicles from cash money. The end-game for cash money has a well-defined fundamental valuation, with low model risk (Fisher quantity theory), whereas the model risk for app tokens and ponzis is vast, and the best case upside potential is much curtailed relative to cash money. All crypto is now primarily a speculative vehicle, but BTC at least has a fundamental economy of some size, and that won't change suddenly.
Secondly, we should distinguish the various levels of maturity of cash money. Gold is mature. Debt-based national currency under centralized management is experimental, but ubiquitous. Bitcoin is unknown to 99.95% of the potential user base, and lacks essential features, and development is stagnating. Monero is unknown to 99.9999% of the potential user base, and lacks essential features, but development velocity is quite respectable. Clearly the growth potential of XMR is much greater than any other instrument in operation today, if you consider the prospect of becoming the primary international medium of financial exchange to be within the realm of possibility.
The best example of crypto achieving bitcoin mcap is bitcoin, and that took 5 years. It takes time for money to flow, and the pipes are narrow enough so that back-pressure prevents too rapid a rise in mcap for XMR. It would take perhaps $200mm influx to bring XMR to parity with BTC. Poloniex can handle perhaps 20000BTC/diem, max, so it would take at least two months for parity to be achieved, if everyone decided today that BTC was utterly uninteresting, and only XMR mattered. So, if XMR will be successful similarly to BTC, with no less speed, it will take between 2 months and 3 years to get there. Meanwhile, there is no particular reason for BTC to decline while XMR ascends. Quite the contrary, in fact, as buying XMR requires first buying BTC. By the time XMR reaches USD 420, BTC will almost certainly pass $1k - unless a reliable and accessible fiat exchange or three opens meanwhile.
Once XMR\fiat exchange is safe and easy, then it becomes possible for XMR to supplant BTC in most if not all of its cash money use cases. Whether it does so will depend on the robustness of the XMR economy, relative to the BTC economy. As the size of both economies become substantial, the speculative fraction of the value of the tokens becomes much smaller, and hence the impact of confidence is much lower. Moreover, the transition of a large economy from one medium to another is not going to be instantaneous, so there is plenty of time for users to adapt. BTC will never go away in any case. It will just be used less. It is likely to continue to grow in value even as it is overtaken by XMR. Only when the XMR economy is substantially larger than the BTC economy does it begin to threaten the value of BTC. And that might never happen, for all we know. I personally consider it very likely, because privacy is only increasing in importance over time, and because XMR is much better able to adapt to changing circumstances, by virtue of its release model and team dynamics.
I have to disagree with extreme catastrophic change models, because there is a lot of inertia and the channels for money flows are so narrow. Huge volatility, yes, always, until the economy dominates over speculative flows. But stuff takes time, and people adapt. BTC has strong advocates, and they will keep using it, and keep supporting its value, for a long time to come, no matter how wildly successful XMR should become.