it won't (yet)
There's too many problems with the Switch that's preventing that from happening, the main people who are buying it are console-styled players, not handheld
The reasons are that
>Its too expensive
330 dollaridoos without games and that's just in the U.S., its worse in other (often european) countries somehow and a lot of the "must-haves" for the system are 60$ or so and are also shit. The 3DS was failing at launch because it was too expensive and that was 200$.
>it has no real library yet nor backwards compatibility, and is far more geared towards console-styled players
The biggest and most notable games for it are all in 3D and feature large worlds or heavy use of multiplayer (Odyssey, BotW, Splatoon 2, ARMs, etc.). Much of the "must-have" games for the system will be 3D and intended to appeal to the console audience (numerous high-profile also ports suggest this like nu-Doom, anything Dark Souls related, etc.), they're trying to consolidate their console and handheld audiences but it remains to be seen how effective the latter will be. It will likely take some of the market away because of how hard they're forcing shit on this system like the new pokemans
They have some indie ports and other shit that you would see on a handheld, sure, but it won't be a handheld until a lot of niche and handheld-styled shit starts getting natively developed for it
>Its ergonomics and overall size
The 3DS XL and Vita were already pushing it in terms of handheld size, able to fit in your pockets still at least
The Switch can't, on the other hand. Its too huge and bulky for a handheld. You can't bring it anywhere without a case (and disassembling the joycons). Its the console equivalent of a "gaming laptop" right now.
Their marketing and first-party games however, has been quite effective for it. They'll pull in most reluctant people with Smash and Pokemon; if the new Fire Emblem and SMT V and whatever other games similar to those are good, they'll pull in some more people from the handheld crowd who see a worthwhile shift/improvement coming in terms of library and don't mind the other issues with the system. I don't see it replacing the 3DS for at least another 3 years or so and by then someone might actually make a real handheld to fill the literally empty hole in the market right now.
Obviously this is quite a simplifying analysis, if you want to examine every facet or point out some "indie game/port that's totally handheld-styled" you can, but there's some concrete facts about the Switch that can't really be argued against as of right now