I have to agree...having the same delay block in all patches is limiting....
TLDR Version:
So, in the end, if you want spillover I would suggest that you build a patch template that includes the delay & reverb blocks in the grid where you want them & then use that template to build all of your patches. That way, your patches always have the delay & reverb blocks in a fixed position in the grid like other devices and spillover will work the way you want it to.
Full Version:
Having the same delay block in all patches is precisely what the Axe would need to have in order to do spillover delay like some other devices do. The reason spillover is "easier" in other devices is because it is a fixed block in their signal chain. You can turn it on or off, but you can't move it. As you change from patch to patch, the delay block is either on or off in that patch & spillover works seamlessly. The downside of that type of setup is, of course, that you can't move the delay (or reverb) block to a different position in the chain.
Cliff made a decision in the design of the Axe to give you complete freedom in how you want to build your grid (signal chain). Any change to the Axe that makes delay or reverb spillover "easier" allows makes the Axe less flexible. IOW, giving you what you want (automatic spillover capability) is actually the more limiting implementation.
So, there are 3 choices, as I see it:
1) Give users the maximum amount of flexibility with their signal chain, understanding that they will have to build presets a certain way to achieve spillover.
2) Dedicate certain blocks in every patch to delay and/or reverb, limiting how users can build their signal chain.
3) Add another dedicated delay & reverb processor to the Axe that is placed after the end of the grid in the signal chain so that it can be used by any patch.
I proposed a way to do option #2 on this forum a few weeks back, but there wasn't any real interest. It creates more additional issues than I think the vast majority of users want to deal it (creates more problems than it solves).
So, solution 3 is probably the only answer that would please everyone, but it would require a hardware change to the Axe. Maybe Ax-FX III, if Cliff deemed it worthy (but his comments so far lead me to believe that he doesn't).
So, in the end, if you want spillover I would suggest that you build a patch template that includes the delay & reverb blocks in the grid where you want them & then use that template to build all of your patches. That way, your patches always have the delay & reverb blocks in a fixed position in the grid like other devices and spillover will work the way you want it to.
My .02