No, no one takes Wilkens seriously. On the most general level this is because his idea is based on a mix of cherry-picked resemblances, arbitary hypotheticals, and outright misinformation. Some of the misinformation comes from over-reliance on translations: all translations fudge details to get across a point sometimes, and if you go putting lots of weight on the fudged details, it's not going to end well. See below for examples.

Moreover, this isn't a situation where there's a vacuum of evidence, and as a result we have to weigh up alternative speculations. On the contrary. We have copious textual, epigraphic, and material evidence. Ancient geographers tell us the exact location of Troy; ancient inscriptions tell us the exact location of Troy; nearby locations that Homer refers to are all in the vicinity of the real Troy; the cult of Ilian Athena that we see depicted in Iliad book 6 was a real thing in 7th century BCE Troy after Greek settlement, and is depicted in numerous coins and inscriptions found at the exact location of the real Troy and its vicinity.

Wilkens' argument is based on ignoring all of this, in favour of hypothetical possibilities.

On to the detailed points you raise.

Tides. Homer does not, in fact, refer to 'tides'. Some translators do, in phrases like 'the tide of battle', but that's evidence of the modern translator's taste for words, not of what Homer was thinking. There is no straightforward word for 'tide' in classical Greek. And where phrases describing tides do exist, we should also notice that ancient Greeks were perfectly well aware of the existence of Gibraltar and the ocean beyond, including in the Archaic period (both Homer and Hesiod refer to fantastic places and entities 'beyond the Ocean').

Weather. Greece and Turkey do experience rain, fog, and snow, and they aren't confined to mountain tops.

Horses. Horses are never used for cavalry in Homer. They exclusively pull chariots. In real-world Greece, at the time the Iliad was composed, horses were used for mounted infantry (only Thrace had horses suitable for cavalry); that's also the function that Homer's chariots serve -- they aren't attack vehicles, they carry mounted infantry. The use of chariots is a false archaism, conveying the flavour of a dimly-remembered past by having a contemporary function (mounted infantry) provided by an archaic aristocratic instrument (chariots).

Oysters. Homer doesn't refer to oysters either. Iliad 16.747 refers to someone gathering tēthea, but it's a rare word and the sense is unclear; it could be any kind of shellfish. Liddell and Scott actually gloss the root word, τήθυον, as 'sea squirt', based on how a later writer uses it. Be that as it may, there are oysters native to the Mediterranean.

'Schliemann's Troy location'. There is nothing 'incorrect' about the location. Contrary to popular belief, Troy was never lost, and was a thriving city up until 500 CE; it continued to be inhabited on a smaller scale after that point until close to the Ottoman conquest of the Troad in the 1300s. Uncertainty only arose when Schliemann tried to conflate myth with reality, thereby casting doubt on the reality.

Trees. Here is a picture of Chios in autumn, one of the places that in antiquity claimed to be Homer's birthplace.

The armada is too big. Yes, and this is why most people think the war wasn't a real event, or at least not on the scale described -- similarly to how no one believes Herodotos when he says that Xerxes' army had two million soldiers. Ancient war reports habitually inflate figures.

Beards. This is a strange one, because ancient Greek men are almost universally depicted with beards, other than figures strongly associated with youth such as Apollo and Achilleus.

Cremation. There's only so many ways of dealing with dead bodies. That means you can't put much stock in resemblances. Cremation is also found in elite Aztec burials: that doesn't mean the Iliad is set in Mexico. Things like this are only 'reminiscent' in the same way that pyramids in Bolivia may remind you of pyramids in Sudan (and for a similar reason: there's only so many ways of stacking rocks).

The word 'Greek'. 'Greek' is a modern English word, so it shouldn't be surprising that Homer doesn't use it. Homer does however refer to Hellēnes, the word used for people of that country in both classical and modern Greek, as well as Panellēnes ('people from the whole Greek world'). Greece wasn't a nation in antiquity, so the norm was to refer to groups and states by cities (Athens, Sparta, etc.), regions (Thessaly, Phthia, etc.) or ethnicities (Achaian, Ionian, etc.). And this is exactly what Homer does. He refers to 'Thessalians', 'Achaians', 'Argives', 'Cretans' and so on. Hellēnes represents a grouping of all these into one bundle. Homer makes the word 'Achaian' in particular do a lot of work: that's primarily because of legendary migrations that supposedly took place between the Trojan War and the time the Iliad was composed. In those migrations multiple ethnic groups got moved around, including the Achaians, so Homer has to do some fudging to try to conjure up a pre-migration ethnographic map.

In closing, I'll re-emphasise my initial point: this kind of argument means chucking out everything that we do know about Troy from ancient evidence, and instead believing that arbitrary hypotheticals must be true, even when they conflict with the ancient evidence.

In reality, as I said at the start, we have copious documentary and material evidence that classical-era Greeks and Romans regarded their contemporary Ilion as the site of Homer's Ilios. With one exception -- Strabo -- who put Homer's Troy a few kilometres away (and thereby created some confusion in the late 1700s when a French diplomat decided to believe Strabo, and got even Strabo wrong).

Troy is firmly embedded in Greco-Roman culture, both contemporary Troy and the legendary Troy of the past. For an assessment of what Troy signified, I recommend Andrew Erskine's 2001 book Troy between Greece and Rome: local tradition and imperial power (Oxford).