Is Annex a viable alternative for a Duchy buy? Like, if one person never buys Annex, and another player always buys an Annex when he would otherwise buy a Duchy, how would they compare? Are those five reshuffled cards worth the extra $3 debt you wouldn't get with a Duchy? You would probably only buy a Duchy when greening, which is when the effect is more useful.
I might try this the next time Annex is on the table.