In a few recent games, my opponent has played a 4-4, with some wider stones on each side, then “blocked the 3-3” with a 3-4 stone next to their 4-4.
Is this “reasonable play”, or is there a general “downside” that once we’re aware of it, then this will become unattractive?
An example: Ladder Challenge: taw(#24) vs GreenAsJade(#18)
Adding a 3x3 to a 4x4 is in some way a bit uncommon, as there are usually better more ambituous,less conservative moves like a keima or a wide extension for example. Now a 3x4 is not that weird compared to a 3x3 as it protects the corner and offer better future connection on a side.
During the opening, the move is probably a bit slow. Generally if you want to play a combination of 2 stones in the corner, you’d prefer a normal shimari like (4-4 + 3-6), (3-4 + 5-3), etc.
The move may sometimes be correct at the end of middlegame, if it’s the last big point and you want to prevent the opponent from invading a big territory (assuming that combination + surrounding stones are enough to prevent an invasion).
Let’s ask AI about this:
if you settle the situation in the left a bit, it’s even -0,3 only - so a really good move
Let’s try that directly in the beginning:
even blocking like this, while not ideal - is very good. it’s “-0,6” pts
so, getting out of bed now, work calls 
Would be interesting to compare with 3x3 using AI?
Hmm I didn’t want to make too precise comments since it’s an ongoing game.
It’s a reasonable move to totally prevent the 3-3 invasion. It’s not unreasonable as in not an overplay, if anything it’s an underplay because a bit slow and inefficient. Tewari argument : imagine you played the 3-4 first, and then wanted to add another move, 5-4 next for high shimari would generally be better than 4-4.
This is a bit different matter:
with an approach move there is more to investigate like the difference with answering at the 3.4 vs a diagonal-contact move on the approaching move, or a pincer…
Looking at Waltheri’s pattern search, it turns out the move has been played many times by pros, including at early stages of the game, for instance:
The AI often prefers another move, but the pro’s move is obviously a good move, losing at most about 1 point according to AI.
Well there ya go … I just learned it’s not only a thing now, but has been since whenever! 
The descent has also been quite a normal move for black in high handicap games for many decades, perhaps even centuries.
It’s also common for black to descend as a territorial reinforcement after having made a large knight 4-4 enclosure.
