This is long term controversial issue. If you think the right answer is obvious you probably haven't dove down to the details, where it's much murkier. See in particular John Forester's _Effective_Cycling_. Forester believes that "cyclists fare best when they act and are treated as drivers of vehicles" and are not segregated from them. There are studies in this area pointing in both directions. One such concluded that putting bikes on multi-use trails makes cyclists less safe. A lot depends on the design of the bike paths, and a badly designed one can increase the risk over none at all.
https://en.wikipedia.org/wiki/Effective_Cycling