I think there are many reasons for the lack of appeal that Fuglsang has to many Danish cycling 'fans'.
First, let me just say that in terms of wins only, I completely follow that SKA has had the better season. Winning 4 World Tour wins (when 2 of them are in the Tour)
is bigger than winning a monument and 3 ProSeries wins, regardless of when the wins were achieved.
If we break down the individual performances, I'd also add Mads P's victory in Gent Wevelgem to the mix. I find that Mads P's victory, the 2 Tour stage wins for SKA and Fuglsang's Il Lombardia triumph are all three equally impressive for a Danish rider to achieve. While both Mads P and SKA had to tactically outmaneuver a tougher opposition in order to earn their victories, Fuglsang won a monument by simply being stronger than anybody else (almost a déja vu from Liege).
Now, does the casual cycling fan see it this way? I believe not.
First, there is the 'problem' that it was Il Lombardia, that Fuglsang won - a race that does not have much identity in Denmark. I do not think that many Danish cycling 'fans' even watched Il Lombardia on August 15th. There were probably more people tuned into Dauphiné that day (another extremely tedious Dauphiné stage, might I say).
Second, as you say he has had a season of consistency with many top results, but only one big win. The dominant victory from Andalusia would be forgotten, had it not been for the pre-race polemics that arised surround the now debunked Ferrari rumour and investigation. Watching Fuglsang take his first win of the season in his first race after the shitstorm he'd been through was quite impressive, but still it is a relatively small race to follow if you are not into cycling on a deeper level.
Third, there is the Leopard-move. The fact that the escape from Saxo Bank effectively ended the team as we knew it has contributed to Fuglsang as a 'Judas' figure in the eyes of many Danish cycling fans. Fuglsang was part of the gang of riders along with the Schlecks, Cancellara and O' Grady, who really embodied the Saxo Bank team back in the days and this team spirit was essentially lost when Contador arrived with his Spanish armada. Still, many Danish fans clung to supporting Saxo Bank but with a sense of feeling betrayed by riders such as Fuglsang.
Fourth, in combintation with the Leopard move, there is the mystique surrounding Jakob Fuglsang. There is this aura around Fuglsang, which is hard to describe. He is a rather detached and quiet figure, who appears complex on the inside. Like he is always hiding a little bit of himself and is secretly laughing of the circus that unwinds before his eyes. He also clearly knows how talented he is and sometimes points this out in more subtle ways. I believe this attitude can come across as arrogant or slightly elitist to many people, especially Danes, who are famous for their quick negative responses to anyone who dare display self-belief. In addition, Fuglsang is born in Switzerland, married with a Luxembourger and he rarely sets his feet on Danish ground - not exactly ingredients that make him the trademark Danish person.
I managed to find this piece from last year, if anyone is interested. It is a tribute (in Danish) to Fuglsang, which describes his qualities from a more intellectual perspective than what is usually heard on classic cycling podcasts.
https://castbox.fm/episode/Fanbrev-til-Jakob-Fuglsang.-Danskeren,-der-kan-vinde-Tour-de-France,-har-givet-mig-lyst-til-at-kede-mig-id489374-id168268195?country=dk