Have you noticed that most people advising you to check it all are not that good at chess?
If anything, you have limited time, energy or patience to play a game so you can't or won't check it all. What you do is to consider most of what makes sense.
When walking through a forest you consider the trees as to not into walk into one, but not as a source of danger. A different story could be if, for some magical reason, some trees may move by themselves. In chess, say you have a King in g1 and a Pawn in g2, while the rival has a Queen in g4: You see no danger in 1...Qxg2+ because the Pawn is defended, although you may consider the consequences of 1...Qg4–d1+. Should you have another Pawn in h2, then the threat of Qg4–d1+ may light up some alarms because the own King may be less secure after the forced 2.Kg1–f2. And you should be worried if Pawns in f2, g2, and h2 because of 1...Qg4–d1++.
So, you don't consider each and every move (not even engines do that since long ago), but use filters to consider only those which make sense. And what makes sense? Whatever and everything which may increase the piece activity (active or potential threats) for one side or the other, with special attention to those with follow-ups as such may evolve into an unstoppable initiative.
Further explanation.
Improving in chess has a lot to do with improving such filters. For example, after 1.e4 e5 2.Nf3 Nc6 3.Bc4 is not uncommon to see a beginner playing 3...h6, because they're familiar with Nf3–g5 with Bishop and Knight coordination against f7. However, that's not the only coordination available for White in such position, and although those others may involve more pieces and tempos, White will be a tempo up in several of them.
A more subtle example to clarify long-term threats: In the closed Spanish, Black usually delays Bc8–g4 until White has already played Pd2–d4. The main reason is that White may answer with Pd2–d3. So what with that? Well, White will follow with Ph2–h3, and force the lose of a tempo for Black, or conceding the pair of Bishops after which White may later threat to open up the central position advantageously with Pd3–d4 or Pf2–f4. And what if the Bishop retreats to h5 instead? In such a case, if possible White will play Pg2–g4 leaving the Bishop out of play should White can develop active play on the Queenside, or Black may find troubles in setting up his pawns and pieces to defend the Kingside (Pg7–g6 followed by Be7–f8–g7 and Pf7–f6 followed by Nc6–d8–f7) because of the misplaced light squares Bishop.
Closing.
If all you want is to not to hang pieces or to take advantage of them, then focus on undefended or inadequately defended material, as Black's Qf8 and Kg8 protecting a Pawn in g7, against White's Nf5 and Bb2. A step farther is to check weakened squares from which the opponent may establish a strong threat (typically a double threat) or coordination, such as in Kg1, Pawns in f2, g3, and h2 when Black can establish coordination on f1, g2 or h1.
Common advice I hear is to always look for all checks, captures, and threats (CCTs). This can help find tactics and avoid blunders. I don't do this, which is probably why I am not a good player. I want to start doing this, but I'm not sure what the correct order should be. After my opponent moves, should I first look at all the CCTs that they would have available if they moved again? Or should I look at my own CCTs first? Also, should I create a list of all the CCTs and then analyze them all, or should I analyze them one by one as I find them?