Can someone explain what is missing in my mental model of the significance of this? Why does it matter than one is an int and one is a float? I understand that

Can someone explain what is missing in my mental model of the significance of this? Why does it matter than one is an int and one is a float? I understand that this means a different range of values and that floats are manipulated differently and with different costs on GPU and CPU because of the way they are stored. Aren't LLMs basically just probability stages, so why does it matter if the values are floats or ints, other than to note that more space for the data gives you more fine grained probabilities? Is this difference mainly to suggest that Google uses different hardware that is more suitable for processing ints and that is a competitive advantage somehow?