Here's a meta-analysis of 97 published randomized controlled trials, showing reliable improvements in cognitive function and transfer to real-world function [1]
Here's an NIH-funded study of more then 2,800 older adults followed for 10 years showing that speed-of-processing training reduces the risk of dementia by 29% [2]
Disclosure: I work at a cognitive training company.
[1] PDF link: https://www.researchgate.net/profile/Catherine_Mewborn/publi...
[2] https://www.sciencedirect.com/science/article/pii/S235287371...