The Probability of Reading "me" in John 14:14

I once posted the observations of Frederic L. Godet, who argues that the "me" in John 14:14 seems to be an "absolutely impossible" reading since it makes little sense to ask Jesus something in his own name. Compare John 15:16; 16:23-24.

Another place that we can find an objection to this variant is the ICC Commentary on John's Gospel by George B. Gray:

This verse is wholly omitted in two minor uncials, as well as in 1, 22, b, ful, the Sinai Syriac, and Nonnus—a strong and unusual combination. The omission may be due to homoioteleuton, v. 14 being repeated from v. 13. ABL and fam. 13, indeed, repeat τοῦτο ποιήσω from v. 13, but אDWΘ in v. 14 replace τοῦτο by ἐγώ. So ADL follow v. 13 in reading αἰτήσητε ἐν κτλ, but אBWΓΔΘ have αἰτήσητέ με ἐν κτλ.

If the verse is to be retained, it must be taken as a repetition in slightly different terms of what has been said already: a construction which is quite in the style of Joh_1 ἐγώ clearly lays special emphasis on Jesus being Himself the answerer of the prayer: “I will see that it is done.”

But the insertion of με after αἰτήσητε, which the best MSS support, involves the harsh and unexampled phrase, “If ye shall ask me in my Name.” No doubt, it may be urged that the man who is in Christ alone can offer petitions to Christ which are certain of acceptance. He whose will is in harmony with Christ’s will, and who therefore can truly pray “in His Name,” may be assured that Christ will perform what he asks. Yet the expression “ask me in my Name” is awkward, and does not occur elsewhere, the other passages in these discourses in which prayers in the Name of Christ are recommended explicitly mentioning the Father as Him to whom these prayers should be addressed (cf. 15:16, 16:23, 24). The Johannine teaching would not indeed stumble at the addressing of prayer to Christ. He who prays to the Father, prays to the Son, so intimate is their ineffable union (cf. 10:30); but, nevertheless, no explicit mention of prayer to the Son is found elsewhere in Jn., unless 16:23 (where see note) is an exception.

We conclude that με must be rejected here,2 despite its strong MS. support; and we read ἐάν τι αἰτήσητε ἐν τῷ ὀνόματί μου, ἐγὼ ποιήσω, the thought being carried on from the previous verse, a special emphasis being laid upon ἐγώ.

See https://biblehub.com/commentaries/icc/john/14.htm