The solution that I've found is to set up your "random encounters" prior to your game session.
But then they aren't very random at all, they're planned.
Since you have a general idea of where your PCs will be traveling in that session (unless they own a starship), you can pick 3-4 types of encounters that they'd come across.
Unless they can teleport. Or unless they have an ally who can teleport them. Or they have access to long-distance flying, or a boat, or they're in a location where plains, a forest, hills and a swamp are all relatively close, or... you get the idea.
While there's nothing wrong with doing as you describe, it absolutely defeats the purpose of actual random encounter charts.
You don't need 19 different encounters on your table: on the D&D 2nd edition tables, 9 different encounters made up 68% of the possibilities.
It sounds like you're proposing a world with a very homogenous population. The 2e charts (the 1d8+1d12 type) were specifically designed to handle the effects of monster frequency (Common, Uncommon, etc.) on encounter chances. Those 68% of the possibilities were more common monsters than the rare ones that appeared on a 2 or a 20.
Which tells me that 2 or 3 of the other entries were just TPKs anyway...
I'm totally going to dispute this. Wilderness adventures, in 2e and before, were specifically higher-level adventures because of the fact that you might encounter anything. On the other hand, the random encounter charts for a 1st level dungeon would be dominated by 1st level monsters; it's just that the ones appearing on a 2 or a 20 would be very rare 1st level monsters.
The main purpose (IMHO) of a random encounter chart isn't to throw specific encounter X at the party; it's to flesh out the world. If you know what lives in the Burning Woods, you can make an area-specific chart of those creatures. Then, when pcs are in the area, they get a sense of a living, breathing world that isn't all about them. Then, when they visit the Feywoods, they encounter different things. They get a sense that this place is not the same as the last place, even though
some of the creatures within each might overlap.
Simply picking every encounter, while absolutely fine, is not the same approach. It is far less of a worldbuilding activity; it is barely reusable, while a random encounter chart can come out every time the pcs are in the area that it covers.