Yes, one of the reasons why I decided to make Chancellor non-terminal was to strengthen Counting House, therefore it also got +1 Buy. But you often do not buy Chancellor because it is terminal and likely collides with your Witches, for example, so why not make it non-terminal. I understand your fear that you need to shuffle your deck a lot, but in many cases you can do that in your opponent's turns and it does not take five minutes to shuffle your deck. Additionally, with a chapel trimmed deck, you shuffle your deck every turn as well, and nobody complained.
I don't think you understand. I'm not talking about shuffling between turns. Non-terminal Chancellor would dramatically increase the amount of mid-turn shuffling.
For example, you suggested a cantrip Chancellor for $4. I play a CantripChancellor, draw a card, get +1 Action and +1 Buy, and discard my deck. Then I play another one. I have to immediately reshuffle in order to draw a card, after which I get another Buy and Action and discard my deck. Then I play another one and have to reshuffle again. See what I'm getting at?
A version without +1 Card wouldn't be as bad in this respect, but it would still cause an immediate reshuffle whenever you drew cards afterward. Not only does that slow things down, but it completely ruins the benefit of deck-flipping. Let's use Witch as an example, since you brought it up. I play a non-terminal Chancellor and discard my deck. Then I play a Witch. I immediately reshuffle because I have to draw 2 cards for the Witch. Now my discard is empty and my deck is full, which means that whatever card(s) I buy this turn (and my Witch) are going to take a very long time to be reshuffled into my deck. That's the exact opposite of what Chancellor's ability is for! The whole point of Chancellor is to get the card(s) you bought this turn (and to a lesser extent, recent turns) into your deck immediately!
Trusty Steed is the only current example of a card that can be non-terminal and flip your deck. But there's only ever one Trusty Steed in a game, and when was the last time you chose [+2 Actions/Gain 4 Silvers]? Usually if I'm gaining the Silvers, I choose +$2 or +2 cards to go along with it, but maybe that's just me.
EDIT: On a related note, I don't recommend deck-flipping abilities if your opponents are playing Witches. In general you want to avoid getting those Curses into your draw pile faster.