This is indeed the case. Rhyme and rhythm are very important in lyrics. Many times, there is no choice but to omit some particles and the like. This is also something that cannot be helped. In fact, this is not the case for Japanese songs, but for Chinese songs and English songs. Just like ancient poetry, songs are mainly about appreciating the melody and artistic conception. As long as the general meaning can be understood, there is no need to study pure grammar.
So, don’t take it too seriously. It’s enough if you can understand it. If you can’t, forget about it. But if you want to learn Japanese, just read books honestly. Listening to music can only help and improve it. Interested, haha~~~