It would also have the benefit of not being part of USA, some of the reason for Michigans trouble today are because its part of USA.
What you're failing to realize is that Michigan was industrialized because it was part of the US. As an independent country, the prospects for that industrialization are very much in doubt.
Leaving aside the copper and timber of the Upper Peninsular, because an independent Michigan would very likely not own the UP, Michigan has
none of the natural resources required for 19th industrialization.
As Meepy correctly points out, other than farm land Michigan's only "resource" is it's location. It lays "between" the coal of Pennsylvania and the iron ore of Minnesota so, with mills and factories in Michigan, the transportation routes for one to the other didn't have to be as lengthy.
You should also note that Michigan's industrialization took place decades after industrialization of other regions in the US because of the transportation systems that needed to be built up. If Michigan were outside the US, the existing borders would make the transportation of the raw materials across them less desirable and the "middle point" between Minnesota's ore and Pennsylvania's coal would be elsewhere
within the United States.
An independent Michigan's only actual resource would be the St. Clair river between Lake Huron and Lake Erie and, if the Canadian border remains the same, Michigan's control of that tiny waterway would not be complete.
If Michigan had been a independent country, the money made from it industries...
Those industries would not exist in the types and quantities they did if Michigan were not an integral part of the US industrial system.
... it wouldn't have seen such a large degree of migration away after deindustrialisation...
Without industrialization, Michigan wouldn't have seen as large a degree of
internal immigration as it did in the OTL so there wouldn't be the population which is supposedly migrating away after de-industrialization.
Thanks to the industrialization it's place
within the US allowed, Michigan saw huge increases in population during the 20th Century. Also, because foreign immigration was limited after the 1920s, Michigan's population growth was due to
internal migration within the US. Between 1910 and 1930, Michigan's population grew over 30%, thanks to almost wholly to an internal US migration an independent and lesser industrialized Michigan would not receive. After slumping during the Great Depression, Michigan's population again grew by over 20% between 1940 and 1960. Again from internal US migration an independent Michigan would not receive.
Finally, with regards to the so-called migration away from Michigan, even with that state's de-industrialization, it's population actually continues to grow. The real difference being felt is that Michigan's population growth is no where near as massive. For nearly seventy years, Michigan's annual population growth averaged over 16% and that amazing performance was looked upon as "normal". Detroit may be a nearly abandoned Rust Belt city, but that has to do with factors beyond de-industrialization and Michigan's actual overall population is still increasing.
So luikely we would see a Michigan which was poorer in 19th century but richer today, if it had become independent.
Because an independent Michigan would not experience the industrialization and subsequent migration seen in the OTL, it would be poorer in this time line's 19th Century, 20th Century, and 21 Century than it was in the OTL. An independent Michgan will be a specialty agricultural producer, tourist destination, toll keeper, and little else.