I couldn't figure out a good title, so I just simplified the problem.
Say you hit a good backhand or forehand down the line from your backhand side (ad court for righties, deuce for lefties), then they hit a short ball crosscourt.
The ball is hit at normal rally speed or a little less, and by the time you get to it, you will likely be hitting the from near the sideline (still inside the court though). Do you always hit this shot down the line (by far the easier shot as you can get your weight forward into the shot), or do you sometimes hit it crosscourt and behind your opponent who likely expects a down the line approach/winner?
Basically, imagine hitting an inside in forehand (running around the backhand getting a relatively clean ball that landed short, and having to run in a forward diagonal across the court to hit it.
Now, if you started from the forehand side of the court and hit this shot, you could easily hit the shot to both sides of the court while getting some weight transfer (since you can get to the ball much earlier, and there would be a less drastic change of direction to get your weight into the ball). If you're very fast and have strong legs (to change directions and push off in the crosscourt direction), you can probably also do it if you started from the backhand side of the court.
So if you were like a strong 5.0+ (or like 5.5+), then you could probably get to the ball quickly enough and have strong enough legs to change go crosscourt behind your opponent. If you were a 3.0-3.5ish, then the ball would be slow enough such that if you ran to the ball, then you could be able to go anywhere on the court with it.
At the 4.0-4.5 level (including upper 3.5 and lower 5.0), with mediocre/solid footwork and mediocre footspeed against a "medium" paced ball, would it ever be a good idea to take the risk to send the ball back crosscourt? Or should you just go with the flow and go down the line because the weight transfer into the shot is a million times easier? You will still always hit a strong shot that requires your opponent to produce a strong shot in order to win the point from you.
I tried it once recently, and felt how awkward the shot was to hit. It did not feel even remotely like a smart shot to ever hit in that situation.
Of course, you could meet the ball a few feet further back, giving yourself more time to settle yourself before hitting the ball, and then go crosscourt, but you've sacrificed about 5 feet of court and hit that ball from a few feet inside the baseline, meaning that all you did was hit a groundstroke that could either set up an easier short ball or be a conceding shot that gave up an aggressive opportunity and reset the rally into a neutral position.
I don't think I'm going to get any faster anytime soon (though my footwork can be better and I'm working on it), so should I just scrap hitting crosscourt in this position or should I occasionally take the risk and hit it crosscourt sometimes when I feel it will be a clean winner? Because if it is an approach shot, I feel like my ability to approach the net would be very slow (you're approaching crosscourt when your weight is moving off the court, just doesn't feel smart).
This is the sequence, but the ball lands shorter and you make contact with the ball at least 5 feet inside the baseline, as opposed to from on top of the baseline like Federer does here: