Yes, they can be a personal device like a game boy, but they can also be a shared device.

The regular Nintendo Switch (and I think the OLED one) can be played handheld or docked (aka. plugged into the TV). I'd recommend this version.

The Nintendo Switch Lite cannot be plugged into the TV, and is also harder to play multiplayer with other people in the same room. So avoid the "Lite".

The controllers on the regular Nintendo Switch are removable. This means that you can buy a console and have two controllers for some games. Some games require more buttons, so each player would need a pair, but some simpler games like Mario Kart or Mario Party can be played with just one half (aka. Joy-Con).

The games are generally sharable between consoles and within consoles.

Between consoles: The cartridges will work no matter how many consoles you swap it between. Only the console with the game inserted will be able to play the game. However, the saved games (progression in a game) are usually saved to a console, not the cartridge.

(The same holds true for digital games only if the account that bought the game is connected to a console. Accounts can be connected to multiple consoles. An account can only be logged in to one console at a time, so ALL digitally-owned games on that account are locked to one console at a time...but if they aren't logged in, then the another console can log in and play the digital games. So no multiplayer, but taking turns playing the digital game on different consoles. Saves might be shared here, though)

Within consoles: Almost every game allows each profile on the console to have their own saved game. So you could buy one Pokemon game, and up to 8 people can have save files for that game. Depending on the game, they may not be able to play simultaneously (e.g. trading), but they can all have their own save files with their own progression.

So, what you suggested is overkill. Here's my advice:

If you want family game time, you just need...

• One OLED Switch (connects to TV)
• Buy games physically if you foresee anyone wanting their own console in the future, or digitally if not
• Check if the games you're buying can be played with a single Joy-Con. If so, the console comes with 2. If a player needs 2 Joy-Cons each, you have 1 controller with the console. Buy enough Joy-Cons or Pro Controllers (which are equivalent to a pair of Joy-Cons, but can't be "split") so that you have enough for all your players.
• This console can still be played handheld whenever someone wants solo game time or when someone else wants the TV.

This will allow everyone to play single-screen multiplayer games on your TV together. Note that most games allow up to 4 players at once. More is rare.

Or, if you've got older kids who want their own individual games that they'll play independently at the same time, it gets more complicated. But here's what I'd suggest.

• Get at least one dockable (non-Lite) Switch in the family. This Switch "gets" access to the TV, but may also have to "share" for family multiplayer time.
• Get Switch Lites for anyone who REALLY needs to be playing something else independently when the TV/"main" Switch is in use
• Get physical games: Any kid can play it in any console, and as long as they're on the console that has their profile, they can continue their saved game. You DON'T need multiple copies of any game except in very rare scenarios.

Having extra consoles is rarely necessary to play games together. The only time they'd need It is if they're playing games online together and the game doesn't offer split-screen. Maybe Fortnite? But then they can take turns, unless you really want to buy separate consoles, lol

Please ask any follow up questions you have. I'd be glad to help clarify anything! Typing this up was surprisingly fun, lol