Why is it likely that the Sea peoples spread from Italy to the Eastern Med? Afaik all evidence points towards Aegean origins (e.g. with that pig DNA study from the Philistines). The Sherden link then would be that these people are the name-sake for modern Sardinians as a result of taking over power from the natives.
In terms of the IE-Tyrsenian link, of course it's speculation, but it has some limited evidence backing it up (not that I understand it). There's also the point of where did Etruscan originate from if not from the Sea Peoples. It surely isn't dated all the way back to Cardial Ware farmers, and it definitely isn't related to any branch of IE in Central Europe. The Sea Peoples are the only real explanation imo (and there's circumstantial things like the Teresh-Troy links etc.). Tyrsenian has been linked with Minoan etc. languages as part of a greater Aegean language family, and that also fits with the archaeology. These people (if the Aegean language family is legit) were definitely Pelasgians, and it just so turns out that the Pelasgians were close allies of Troy.
I do thrive on all of this stuff, I'll admit, but I'm a big believer against coincidences (and things like e.g. independent inventions). Even if my idea isn't the truth, I reckon there's a link.
Also, I don't think spread of people always correlates with spread of language - the main idea I've been speaking about over the past few months is that the R1b Bell Beakers were originally non-IE and merely adopted it from the cultures they moved into.
Villanovan culture has nothing to do with bronze age Anatolian cultures or with the Aegean cultures in general. There were movements from Central Europe and the Balkans, this is pretty clear looking at the Protovillanovan and Villanovan culture whose material cultures were clearly influenced by the Urnfield culture and Hallstat culture respectively, but there's no influence from Anatolia, at least by looking at the archaeological record. Even looking at the imports during the Villanovan period the imported objects mostly came from Nuragic Sardinia and later on from the Greek and the Phoenician colonies.
And as for the Sardinians their material culture was still Nuragic during the late bronze age and early iron age with nothing in common with the late bronze age or early iron age Aegean, the few external influences which were confined to metallic artifacts came mostly from Iberia and to a lesser extent Cyprus.