Excel's limits are 16384 columns and 1048576 rows.
I'm talking wimpy hardware here, I admit. Basically, VirtualBox VMs on a quad-core i5 box with SSD and 8GB RAM. With the VM having three cores and 6GB RAM. But it was the same wimpy hardware for Windows 7 and Ubuntu.
Depends on the file format. An XLS or XLSB file can contain special markers for where each logical row starts, so it can randomly access rows; Both also can persist "calculation chains, which are a simplified dependency graph. The binary formats also store formulae in a parsed representation allowing easy scans to see what cells have to be inspected if a file needs to be recalculated.
But now you've got me thinking, it would be nice if libraries like Dask could allow for flagging of symbolic operations like this to be written to disk for quickly saving metadata where intermediate steps don't explicitly need to be saved.