Cut tape is a necessary evil for small amounts of project-specific components, of course. The problem is you have to store the cut tape in something you can label. It's a redundant amount of packaging and handling, IMO, for generic, non-directional parts. I have tried sticking labels right on the cut tape and put them all in a box, but this creates a tangle of curly cut tapes of different lengths and does not sort well.
Due to the directionality, I leave most all my multi pin IC's on the reel/tube/cut tape, as well as SMD LEDs and diodes. For SOT and LEDs/diodes, I do the tape trick. But for these kinds of parts, I usually am taping just one component tape to a plaque, instead of combining all the parts for a particular PCB. So I have a little board with ~200 SOT 23 signal NFETs on it, another board with PFETs, another board with SOT-23 Schottky diodes, etc. When it runs out, I removed them and replace them... 200 at a time. I minimize handling of cut tape, and it minimizes mistakes, without having to look for an arbitrary label printed on top of an ant that is going to be different on every order of such parts (because I buy w/e is cheapest, and even for the same component, the SOT label often changes between lots). For tubed IC's, I built a tray that holds up to a complete tube of SSOP IC's in 5 slots. SSOP of QFP are my preferred IC package, if I'm going to assemble it myself.
Some of my methods are probably overkill for the average hobbyist. Test tubes for jelly bean resistors and caps is, I think, not. I was doing the test tube thing for many years of tinkering/design before I took on any significant assembly.
Another trick I learned from doing high volumes is for getting cut tape from reels. Cut the tape only halfway through, to the little hole. Then fold it over on itself to measure out and make the next cut. Then fold it over again at this new spot so you get 2 more measured cuts. Then the next time, you get 4, etc. Then stick your cut tape accordion in a bag or a large test tube for when you need to refill a plaque.