[giucal]

I think they don't matter because:

1. they are all fixed or bounded quantities;

2. all algorithms are subject to them.

On the other hand, in practice, the input size is also bounded. You deal not with arbitrarily long arrays, for example, since memory is not infinite.

So, I think, asymptotic time complexity is meaningful as long as the inputs we are considering can grow so much -- while remaining bounded -- that a linearithmic algorithm indeed outperforms, say, a quadratic one for a large and relevant class of inputs.

And that may be why computational models make those assumptions; but I'm not remotely sure.