You can answer this yourself by looking at historical charts of average fees and checking out how much congestion Bitcoin had historically.  The charts do not look good.

Bitcoin became more congested over the years as it grew.  It took longer to clear congested mempools, fees became higher and higher, people started paying to be put on a priority list by miners.  This was not SUPPOSED to happen but it unfortunately seems to get worse every halving.  Others can cope as much as they want, as long as this problem is not solved Bitcoin will become less interesting to many.  It becomes extremely annoying when you have to spend and the mempool is so clogged up your transaction has to wait hours or days and still require two to three fee upticks for it to finally go through.

By bitcoin network becoming too big, I honestly don't understand what you mean because if we are talking about bitcoin's network, it is already very massive like someone else have mentioned here, you can know this if or when you want to run your own node and need to download the full bitcoin blockchain from the very beginning to the very present, you will have to have a computer with no less than 2 terabytes of data space so that after you are done with the download, you will still have some space left so that the machine can run optimally.

But if what you mean is if the bitcoin network become too congested, like many millions of people are transaction on the bitcoin blockchain at the very same time, well, what this will do is that it will definitely lead to the network becoming congested like we have seen on some occasions in the past, this congestion will lead to hiked transaction fees and hiked time one will have to wait to get his or her transaction confirmed.

I don't think we can expect a solution overnight if that situation occurs in the future, so anticipating such a scenario and preparing for it earlier is the wise action. I don't know what are the current developments are on the way targeting the network speed faster but I can assure one thing, Bitcoin will never be suitable to handle thousands of TXs per second so we can't assume that it will replace the current system since we don't even have the solutions yet.