Norwegian moose,
Yes, diet is the main issue. The southern islands of Japan are subtropical and warm enough to allow several of the plant species preferred by the proboscis monkey to grow with little protection. Indeed, some of them grow naturally in Japan's Okinawa islands (which also are warm enough to support coral reefs). Because it is a single country and the distances are relatively limited, transport is easy. When you try to cross borders with plants there are a whole range of issues that have to be resolved (customs), making it more problematic and time consuming. This combined with the much longer distance prevents easy transport of fresh (not frozen) leaves year-round to Europe.
Yes, you could grow the plants in a greenhouse, but here you have to consider the economy. The proboscis monkey is a large monkey and like other folivores it eats a lot. Several kilos per day. It also has a preference for quite fresh shoots. To cover the year-round feeding of a proboscis monkey group (even a smaller one) would require a very large greenhouse. It would be very expensive.
If you wanted natural foraging on the plants in a rainforest hall, as it seems you suggest, it would require a huge hall. I guess a place like Leipzig's Gondwanaland (the worlds largest) would be big enough, but then most of it would have to be reserved for a single species, the proboscis monkey.
Here it is important to keep in mind that the proboscis monkey has a much higher "wow" factor for zoochat users than average zoo visitors. I'm sure most average zoo visitors would love to see the species, but if they were given the following list and had to choose, I strongly suspect the proboscis monkey would get the lowest score: Polar bear, gorilla, proboscis monkey, elephant and rhino. This alone limits the amount of money a zoo realistically could spend on keeping them.
I might add that the climate of Florida is suitable for several of the plants preferred by the proboscis monkey. Zoos in this region would have a clear advantage compared to zoos elsewhere in USA or in Europe. The Florida zoo would have to start a good sized area with suitable plants some time before the first proboscis monkey arrived, but it would still be much cheaper than trying to do it in large greenhouses in colder regions.