If we dissect what is transpiring and the reasons why, maybe we could arrive at an answer to your question.
Praying intelligibly occurs when the soulish part of man is engaged in prayer. This takes place in the mind. The mind can process the words both to understand and to speak.
“What am I to do? I will pray with my spirit, but I will pray with my mind also; I will sing praise with my spirit, but I will sing with my mind also.”
1 Corinthians 14:15
Now the spirit praying can also pray intelligibly. The advantage is the person understands what he is saying. There is a disadvantage however praying with the spirit intelligibly, namely going through the mind. The mind unlike the spirit is not regenerated, it is being sanctified. The mind is limited and influenced by the flesh. Human logic can override the prayer of the spirit and change, alter or deny the prayer being prayed intelligibly by the spirit.
The spirit however has the ability to bypass the mind and act directly on the body. In doing so it doesn’t allow the mind to corrupt the perfect prayer of the spirit. This is done by praying in an unknown tongue.
“For if I pray in a tongue, my spirit prays but my mind is unfruitful.”
1 Corinthians 14:14
Therefore in light of how pure and perfect this praying is, it is highly recommended that praying in tongues take place as often as possible. The spirit needs an outlet to speak to God. By stifling the spirit, when at last the spirit is given a chance to pray out loud, it usually comes out like a hydroelectric dam and it’s overwhelming for the soul (emotions)
“For one who speaks in a tongue speaks not to men but to God; for no one understands him, but he utters mysteries in the Spirit.”
1 Corinthians 14:2
“The one who speaks in a tongue builds up himself, but the one who prophesies builds up the church.”
1 Corinthians 14:4
When the spirit is praying, given only God understands, it is obviously directed towards Him. And since it’s a perfect prayer, it should be encouraged as often as possible. Paul certainly practiced speaking in tongues “excessively” by today’s standard.
“I thank God that I speak in tongues more than all of you.”
1 Corinthians 14:18
This should not be limited only to praying in the closet, private praying. The spirit should be allowed to flow, throughout the day.
Paul makes this point later in the chapter
“If, therefore, the whole church comes together and all speak in tongues, and outsiders or unbelievers enter, will they not say that you are out of your minds?
If any speak in a tongue, let there be only two or at most three, and each in turn, and let someone interpret. But if there is no one to interpret, let each of them keep silent in church and speak to himself and to God.”
1 Corinthians 14:23, 27-28
The bolded parts seem to contradict. You can’t be silent and speak. What Paul is saying is this, no one is to take up time during a church service to merely speak in tongues without interpretation. It isn’t edifying to the church only to the individual praying.
“Nevertheless, in church I would rather speak five words with my mind in order to instruct others, than ten thousand words in a tongue.”
1 Corinthians 14:19
Therefore when he says “speak to himself and to God” he means in a setting when it’s not disruptive to the church service, taking up time with unintelligible speech. But if there is communal praying that could be a time to pray in tongues, or at home, at work, whilst traveling to and fro.
If this doesn’t answer the question, please let me know how to edit my response