I often find that phisicists and cosmologists make use of Planck's units. I have read propositions that sound like
"...at the level of Planck's units many law of physics break down"
"...Planck time, the smallest observable unit of time...before which science is unable do describe the universe"
"... it would become impossible to determine the difference between two locations less than one Planck length apart"
even in string theory:
"* Planck length is the order of magnitude of the oscillating strings that form elementary particles, and shorter lengths do not make physical sense*".
Notwithstanding this and the fact that in QM (almost) everything is quantizied (discrete) I read that in mainstream they are still considered not discrete, cf. Phys.SE link.
I am not particularly aware of any pros, I see only cons; can someone tell me what are the compelling reasons to consider spacetime not discrete? Is it a requisite of relativity? As a corollary, I suppose that they must be both discrete or non discrete, right?