That's not the way I see it when you look at the verse in context. 1 Cor 13:1-3 consists of 5 parallel statements to emphasize the worthlessness of having spiritual gifts without love. Paul is pointing out that even if someone possessed spiritual gifts to the highest conceivable degree, but not have love, it would be to no avail. Each of them is a IF statement, where he presents 5 extreme hypothetical examples to make his point:
"If I speak with the tongues of men and of angels, but do not have love, I have become a noisy gong or a clanging cymbal."
Even if someone had the gift of tongues to such a degree that they spoke in the language of angels, but didn't have love, it would be worthless to them.
"If I have the gift of prophecy, and know all mysteries and all knowledge;...but do not have love, I am nothing."
Even if someone had the gift of prophecy to such a degree that they knew ALL mysteries and ALL knowledge (ie was omniscient), but didn't have love, it would be worthless to them.
"and if I have all faith, so as to remove mountains, but do not have love, I am nothing."
Even if someone had the gift of faith to such a degree that they could remove mountains, but didn't have love, it would be a worthless to them.
"And if I give all my possessions to feed the poor, ...but do not have love, it profits me nothing."
Even if someone had the gift of giving to such a degree that they gave ALL their possessions to the poor, but didn't have love, it would be worthless to them.
"and if I surrender my body to be burned, but do not have love, it profits me nothing."
Even if someone had the gift of giving to such a degree that they gave their own life, but didn't have love, it would be worthless to them.
None of these extreme hypothetical examples represents the normal operations of those gifts, including speaking with the tongues of angels. The statements are clearly presented as parallels, so you cannot say one is to be taken as being the normal operation, while the others are not.
Notice that in each case Paul prefaces the hypothetical with the the normal operation of the gift: "If I speak with the tongues of men...", "If I have the gift of prophecy...", "if I have all faith...", "if I give...". So the normal operation of the gift of tongues is to speak in the tongues of men (not the hypothetical tongues of angels).