It sounds like there are a few things at play here:
Product vs applications vs Project
That many products sounds abnormal - certainly difficult to maintain. Usually when I see people say they have so many products, they really mean applications or projects. There are two things I usually find helpful in discussing a product: first, what does the customer think? Would your customer say that your product is data analysis, or cardiovascular data analysis? And second, it your approach similar between the different types of data analysis. They don't have to be the exact same, but similarities in approach mean that improvements in one area can carry over to others if you treat them as 1 (or fewer) products). Think of Microsoft Office. Word, Excel, and Powerpoint all work very differently, but there are all ways to create documents of some sort or another and treating them like one product has huge advantages.
The Benefit of Teams
What you describe doesn't sound like a team. It sounds like a group of people who happen to share an office. A proper team can benefit from more flexibility as well as increased productivity. For example, if more work comes in for one type of work than another, a team can pivot their attention to field that work, but the setup you describe must force those projects to wait. Also, most work that a team takes on has some forms of repeat work between tasks. Often times teams working together can handle this work more efficiently so they gain higher productivity.
Where Teams Don't Work
If the work is radically divergent, it may be that each type of work requires complete attention and all of a person's time to keep up with developments in that type of work. This is very rare - usually only effecting bleeding edge research, but I don't know what kind of work you're in, so maybe this applies.
Scrum is designed to help teams solve complex problems and iteratively develop products. It isn't that Scrum won't work for other things, but this is what it really excels at. If this isn't what you are doing, there may be better approaches for you.