Iron Dome was probably designed for hundreds but not thousands of missiles. They can make a better system able to deal with thousands and the opposition will try ten thousand, it never ends. Actually, you can add drones now. Israel has way more military power than several other much larger countries, this is why any sort of "response" ends demolishing buildings and killing thousands of civilians.
A single missile costs $100k Hamas rockets are much cheaper. They use cheap Qassam rockets that can be manufactured with basic tools and cost less than $1k.
They also buy old Soviet Katyusha rockets and newer Grad and some modern ones supplied by Iran.
Each Iron Dome battery has 20 missiles loaded and needs time to reload.
According to Wikipedia Israelis have between 10 and 15 batteries deployed.
This means that at most, with full capacity and 100% accuracy, the system can stop 300 missiles.
Hamas claims to have launched 5000, but other sources say 2000 unguided rockets. There was no way to stop that many, which is why they launched all at once. They knew it would overpower the defense system.