Your problem isn't with tokens, but with "language". Tokens have little to do with language, other than usually being consumed in sequence, but that's true of anything that has to span over time. Thinking of tokens as letters or subwords is mistaking the general with the specific. We may have started with letters and words and subwords (trying to find the best balance for training), but then people figured why not add pixel patches to the dictionary, and then sounds, and then other signals, and after iterating on it a bit, we now have image and sound and symbol sequence data all being part of the same token space.

LLMs stopped being about "language" - in the sense of English, or C++ - long, long time ago. We're still using tokens, but they're more like quanta of sensory input now.

You can take it in two directions, I guess - either consider "Large Language Model" to be an anachronym, a name that couldn't keep up with times, but we got used to it back when it made sense, or alternatively, just broaden your understanding of "language" to encompass any pattern of quantized sensory inputs, regardless of modality :).

(Given how we know humans can communicate with pictures, gestures, body language, noises, movement, actions, or even gaze, and that when it becomes common enough, such systems develop their own pattern structure - dare I say vocabulary and grammar - and that none of it requires or usually involves going through a "normal language" intermediary - I'd lean towards the second direction :)).

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ETA: also wrt. "thinking with tokens", LLMs don't really think in tokens. You may have heard that phrase, that may have been coined by Karpathy, that "for LLMs, tokens are units of thinking". It's a useful shorthand to remind people that prompting models to be terse and skip prose is effectively dumbing them down, but it's also a bit misleading.

A better analogy is that tokens act like clock signals: each consumed token causes certain amount of computation happen in the network, much like a single clock signal in digital electronics, or turning a crank one revolution in a mechanical contraption. This makes tokens "units of thinking" in the sense that processing N tokens causes M amount of computation to happen. Now, for whatever problem you're solving, there is a minimum amount X of computation that is required to solve in correctly, and it's mathematically impossible to do with less. So if you ask an LLM to solve it, it needs to process at least as many tokens as it takes for M = X. If you force the model to be so terse that it makes M < X, you literally make it impossible to succeed. In practice, you need M >> X.