This is a common question and the truth is, no. Even with crosspicking, there are phrases I can only play starting on a downstroke, and only on certain strings, because that’s how I worked on them. If I want to change which string, or reverse the picking, everything changes and I have to work it out all over again. I have to know exactly which pickstroke starts each string, and I have to know exactly where all the downstrokes are located so the hands can be synchronized.
Over time, the more stuff you work out, the bigger your vocabulary of memorized movements becomes. They you can take those movements and apply them to different fretboard shapes. But it all must at some level be memorized, or you will not be able to play those shapes on the fly.
This homework is the same for crosspicking as with any other of the picking systems we look at. The only difference, is that you have slightly more flexibility with the left hand shapes that you choose. But the amount of the work, and the time it takes to do it, is the same for each technique.
And there are times when crosspicking takes more work, if you want to use accents, pulloffs, sweeps, or slides. Systems like dwps have those movements memorized. For example, a three-string sweep plus an upstroke is such a common shape in dwps, that it quickly becomes memorized. Because of the sweep, this gives you instant access to double-time triplets / sextuplets, which are super common in bop for example. To do this with crosspicking, you’d have to work that out first. To add a pulloff, you have to memorize which pickstroke you come back on when you start picking again. In dwps, you have probably already done that work because it was necessary.
Anyway, in actual practice, the difference in freedom and work is small or arguably negligible, and there are many cases when you would choose the pickslanting technique over the crosspicking technique for musical reasons.
It’s just a tool for a job!