The old cartridges held the data uncompressed. In read only memory that slotted directly into the system bus. There was no loading the game after pushing the cartridge in.

Modern systems have data with multiple compression formats. Held in hierarchical file systems accessed through separate devices on the system bus. That don't have the speed or latency of system memory. And even compressed modern games still take up to 3 million times more space than old cartridge games.

Simple version: it’s not actually “loading” anymore. It’s loading (pretty fast), decompressing (not very fast), and in many cases precomputing (potentially very slow). Current cartridges are storage for the same kind of data that was found on CDs and other media, just in solid state form.

OG cartridges, as was pointed out by someone else, were not doing any of those things. They weren’t even always exactly just storage, they were basically a black-box addition to the logic board. In fact, some cartridge games included entire additional processors that were looped into the logic to provide additional processing power for graphics or audio. That’s what Super FX on the Super Nintendo was: a math coprocessor in the cartridge that helped handle 3D graphics.

I’ve often wondered that as well. I can copy a file the size of an entire game cartridge across my home LAN in the time it takes some games to load the welcome screen.