You are not the first person to think of this. Mechanical keys have been around for centuries. Lock makers unsurprisingly have learned a thing or two in that time.
There are nowhere near as many as 100k different combinations on a standard key. For things like the Yale and Chubb locks that most people have, you're talking about 5 positions on a key with 5 different depths on them. A lot of combinations just aren't mechanically sound (like very deep cuts next to very shallow ones) so I'd hazard that there are about 2000 - 2500 differnt viable combos. Whilst not impossible, you could theoretically cut youself every single combo - which would weigh an absolute ton and try them all one after the other. Best case scenario, you're talking about 3 hours standing there trying keys on a door - assuming that there is only one lock on the door.
What really changes things up is that not all keys fit all locks, and keys vary wildly. Whilst Yale cylinders are certainly very popular, so are Union and Era locks. To the untrained eye, they look the same - but one key will not fit into the keyway of another. There's a slightly more secure brand called Ingersoll, which has three different sections of double bitted keys, none of which fit one another. When you next walk past a key cutting place, look how many keys there are hanging up behind the counter - that's only a small selection of what actually exists. A lot of locks fitted by locksmiths and security companies have unique profiles, only available to them. Some high-security keys have different mechanisms allowing for tens of thousands of different combinations. There's a brand called Kaba that uses perpendicular holes drilled directly on to a flat key - and up to 26 different rows of pins in varying angles and with multiple pin depths, you'd be talking about a number of viable combinations in the n^20 power. Security keys are also not commercially available - so you wouldn't be able to buy the blanks easily and it would take you longer than the lifespan of the universe to cut them, let alone try them on a door. I also doubt that there is enough matter in the universe to make that many keys. Such keys also have active components on them (moving parts in the key itself) to prevent copying via 3D printing.
Having said all that - certain types of keys - Union 2 and 3 lever keys that you usually find on old-fashioned internal doors; only have a 50-200 differs at most, and its not unusual for caretakers or locksmiths to have large rings with all the different keys on them and if a key gets lost, that's probably the quickest way to get the door open.