Actually, I fought a cheap arbor/cheap chuck combo for a couple of years. I actually had the chuck fall off the arbor and land- spinning, with a drill bit- practically in my lap.
The two tapers (the male on the arbor and the female in the chuck) were ground incorrectly, and there was only a narrow ring of contact.
I eventually got it reasonably reliable with loctite and a big hammer, but later, when I got the Grizzly, I invested in a real live Jacobs (as in the brand) arbor and a Jacobs 14A "Super Chuck". The chuck, as I recall, was north of $100, and the arbor probably another $40 or so, but it's been 100% reliable and very concentric from day one.
I keep saying it, because I've lived it: Spend a bit more and buy quality tools to start with.