Any drawback to keeping the drum spindles on my 66 Valiant?

I wouldn't use 9" drum spindles for anything. The small diameter lower ball joint bolts have been known to shear off, even Ma Mopar got rid of them well before getting rid of front drum brakes. The 10" drum spindles used different lower ball joints with larger ball joint to spindle bolts.

That being said- the later disk spindles use larger wheel bearings, which not only increases the strength of the spindle but increases the bearing surface as well, both are nice improvements. The larger upper ball joint is also a strength improvement. I haven't heard of a small upper ball joint failing though, so the added strength there really isn't a safety issue. Another thing to consider is that all of the factory engineering was done for bias ply tires. By the time the factory swapped over to using radials, they had already implemented the larger upper ball joints, thicker spindles, larger bearings, and larger bolt pattern with larger diameter studs. So while there are plenty of folks running converted drum spindles with disks without any issues, if you're going to say "they came from the factory that way" then you should consider the factory probably wouldn't have made them that way if they were going to have radials. Just food for thought.

As for the SSBC kit, I've never understood it. They're mostly just OE '60's Mustang parts, there's really nothing fancy about them. You can use the '73+ Mopar disk conversion just as easily and for a similar price, and all your parts are off the shelf. With SSBC out of business, there are some parts you either can't get or need to have modified to work.