Well, destroying USD was the plan when creating EUR.
EUR is taking about 2% yearly from the market, but at this rate, we need again maybe 20 years to get USD replaced. Unless something geo-politic happens, like US vs IRAN for example...

it would, if euro banking doesnt hast the gambling nature like usd banking, everything will be different.

I doubt that Euro will replace US dollar as the world reserve currency. Instead, Bitcoin might be the replacement. Although the US has been heaping up too much debt without paying, an analyst once postulated that the US dollars is technically backed by crude oil. Let's see how the economic war swing. I expect bitcoin to rise the more to meet the trade war.

Who knows. Maybe this will happen in the long term future, but I don't really think that this is something that is likely to happen even in the next decade. The influence of the US dollar is still very widespread, especially in foreign countries.

Also, even if Euros do overtake the US dollar as the world's dominant reserve currency, I doubt that it'll lessen the demand for USD by THAT much. Thus, it'll likely have less impact on BTC/USD prices as you expect, imho.

If we are talking about the long term, though, all fiats are trending in the same direction as their intrinsic value given the fact that they can be printed infinitely, theoretically. BTC's relative value to them should climb in the long run, as long as adoption levels climb as well, or even stay the same.

Even if we assume that this happened and that the USD value tanks (which isn't necessarily a given), Bitcoin should still trade for the same general fiat value, maybe higher on USD and lower on EUR but still according to the two currency's exchange rate with each other. I don't see it affecting Bitcoin's value in any signifcant way, so why does it matter?

your mistake is that you think US dollar is giving value to bitcoin! whereas just like anything else bitcoin has its own value measured only in fiat  currencies because that is what we use to measure literary everything else. so if US dollar were to crash, then bitcoin value against US dollar should rise up equal to the amount of the crash.
similarly when bitcoin is worth 1 in dollar and 10 in another fiat currency, if that fiat value tanks and has half its value then bitcoin should be 20 in that other currency. as an example you can look at the fiat currencies that tanked over the past year and how bitcoin went up against each of them.

Euro is weak because it depends on many small economies. Where there's many members there are different opinions and arguments. Some countries perform better others worse some may even exit the union like GB. Euro will react to each and every small problem within the union.

Now it's gaining value but that won't last forever. There are better and worse years in the life of every company and every asset.

  I don't get how it will be any different for us.

Bitcoins in dollars and Bitcoins in euros will remain same regardless , it doesn't depend upon the dollars to be honest , it has its own price which is globally same in each Currency.
Therefore no matter how up or how down it goes it is going to be same regardless .

The only thing that will change is people checking the today's price or Bitcoin in probably euros but to he honest most already check in their native currencies.

The chance of happening it is really grim! I understand that EUR has become a great competition for USD since the day Eurozone decided to come together! I won't say that EUR doesn't have the power to overcome USD, because they really can do that! However, there will be no impact on the cryptos as such! Just the calculation parameter will be replaced while maintaining the same purchasing power! We are now calculating crypto prices on USD now which will just be replaced by EUR.

I think Trump has worsened the situation of USD by starting useless trade war with China. The world will probably would not give into the dominance of US anymore and that gives a great chance to Putin to increase the dominance of Russia with their allies! A lot more surprises will follow!

I do not think it will happen so soon that the euro will replace US dollar as a global currency, maybe in next 20-30 years from now, provided that the EU does not fail until then. USA is too strong, and I doubt they will lose power just like that, and with Brexit EU it just became even weaker than before. Not only do I think it is weak in some economic sense, but and in the sense of defending its borders from danger from the east.

All countries on the east EU border ask help from USA, which is funny since they should ask help from Brussels or Berlin, but they show how powerful EU is when Putin is picking which part of Ukraine he will take. Some say EU is so military weak that Russia can knock on Berlin's door (like in 1945) before any more serious resistance comes up.

Regardless of some data and speculations, EU is too weak to impose Euro in front of US $, and eurozone is a very fragile creature - just remember the Greek crisis.