If you're immunocompromised (HIV positive, a transplant patient, on immunosuppressants for lupus, ...) you might need to be that rigorous. Most hikers don't have known immune system problems. For the fortunate majority among us:
Filtration alone is likely to be perfectly adequate. The filter will remove protozoa (Giardia, Cryptosporidium, Entamoeba histolytica...) and bacteria (Shigella, Salmonella, E. coli, ...) which are the things that are likely to give you the most trouble. It doesn't remove viruses, but unless you're immunocompromised, you're not likely to get a life-threatening virus from surface waters in the eastern US. We don't have monkeys that carry hepatitis A or polio - and very little of either in our human population.
Aqua Mira alone is also likely to be adequate, unless you're in an area with a known Cryptosporidium problem. It's decently effective against Giardia and Entamoeba if you give it the full contact time or longer. Crypto is rather more resistant, but it's pretty rare. It's effective against all the common bacteria and viruses.
When some of us talk about carrying Aqua Mira as a backup to a filter, that doesn't usually mean using both methods on the same water. Filters have been known to get clogged, crack, freeze, or spring leaks, and a couple of phials of Aqua Mira is less weight than a second filter. If a filter freezes, it's likely worthless because of microscopic cracks that it got when the water expanded inside it, and needs to be discarded.
A much more important principle: wash your hands. Hand-to-hand and hand-to-mouth transmission is how most of these things spread. Soap if you can, hand sanitizer if you must (because of water shortage - there's no excuse for not carrying soap). And do it often. The tree that you just grabbed onto to get up a stream bank, or the shelter register you were just reading, were handled by God knows how many hikers' unwashed hands before you.