Everyone I know, even the cheap types, keeps some kind of wired Internet. It is usually faster than wireless and always cheaper per GB. If you were an EXTREMELY light user I suppose you could go all wireless all the time, but even for the casual user who likes to surf the web on a daily basis and watch cat videos, you'll easily use more data than a wireless provider is interested in letting you have cheap and they'll charge and/or throttle.
Simple example: T-Mobile gives me phone, text, and 1GB of data for $50/month. It would run me $30/month more to get unlimited data (they'll throttle if you get too excessive though). That's for a single device, and gives 7GB of tethering. Speeds are in the realm of 40mbits max, 20-30mbits normally. So that'd work only if your phone is going to be the one-and-only device you use for most things, and do a little surfing on something else. If you want to add a tablet to it you'd be talking adding another line/device which brings it up to about $100/month with 10GB of data per device.
Ok well then having a look at the cable company for about $60/month they'll sell you a 50mbit connection with a 350GB soft cap (meaning if you go over they complain at you and try to upsell you, they don't charge or throttle). You'll really get those kinds of speeds too, pretty much all the time.
That's more money, but not a ton more. Presuming you would have the basic phone plan anyhow you pay about $30/month more than the unlimited or $10/month more than the two devices. With that you get a faster connection, the ability to connect as many devices as you like, enough data to watch Netflix, download games, and so on. Also, you can, of course, upgrade your speed. They'll happily sell you 100mbit or 300mbit for a bit more per month (about $75 and $100 respectively) whereas the mobile speed is what it is.
Not surprising then that all the people I know keep a wired connection. Personally I don't find I need much LTE data, I use WiFi most of the time at work and home, so the 1GB cap is fine for me (more than fine actually) but I need a lot more on another connection. Looking at my usage I used about 350GB last month. Not the kind of thing a wireless provider would be ok with.