Transcribing is a different type of practice than practicing recognizing isolated intervals, and it's also different from sight-singing, which is going the opposite way (from symbols to sounds). All three of these activities can be useful, and they all complement each other.
Transcribing is in some ways easier than hearing isolated intervals. Part of this is because if you know where you are in the key, you can usually rule out a lot of possibilities. E.g., if you're in C, and the tune moves up a step from F, you can pretty much anticipate that it's a whole step to G, not a half step to Gb. There is also usually a huge amount of repetition in music, and a huge amount of real-world music is certain patterns that you can recognize, e.g., a major scale, an arpeggiated minor triad in first inversion, a fragment of a chromatic scale, or a descending 8-5-1 (dropping an octave).
Another thing that tends to make transcribing easier is that you have two strategies for recognizing a note: you can recognize it relative to another note, or you can recognize it relative to the tonality. For instance, the sound of 7 going up a half-step to 1 is very easy to recognize, because you have that feeling of landing on the tonic. Another example is that often in major, you'll get sort of a pop-music cliche where minor iv is substituted for major IV. This is a very distinctive sound, and when you hear it in the melody, you pretty much know you have a b6.
Because the tonal context makes interval recognition easier, there is a pitfall, which is that people will learn to recognize intervals by memorizing how they occur in certain songs, e.g., "My Bonnie Lies Over the Ocean" for a major 6th. The problem here is that in this tune, the major sixth is the 5th scale degree going up to the 3, but what happens when your brain has to recognize a major 6th that occurs as 1 going up to 6? It may refuse to recognize it because of the different tonal context.
Compared to transcribing isolated intervals, transcribing tunes is more relevant to real-world practice if you're a jazz musician. On the other hand, if you want to, e.g., learn to sight-sing atonal opera music, you probably want to make sure you can also recognize intervals without any tonal context.