I really do not understand why they did away with this feature. I prefer my apps to be updated manually rather than automatically, and it would have been nice to have a counter on the live tile with the number of updates available.
re:
I really like TinyDo, but it lacks Cortana integration.
I reached out to Wunderlist a while back regarding live tiles on W10M and they said it's in the works. Probably not a high priority for them, unfortunately.
Does Edge support this? Had sites such as the Verge, BGR and WMPoweruser on WP8.1 and they all had live tiles with revolving headlines, but when I pin these sites on W10M I get a logo of the sites.