No, not at all. The tests of the young child are just to check that he is a continuation from the previous Dalai Lama, not a test of intelligence.
The current Dalai Lama had academic leanings from a young age and impressed everyone with his answers in his Geshe exam as a young man and has continued on that path since then. So, he is very learned in Tibetan Buddhism. He is also quick at understanding topics in modern science and often involved in dialogs with scientists.
While - he's not especially good at spoken languages obviously - even after decades of speaking English, there are many Tibetan lamas who are far more fluent in English than he is.
A Dalai Lama is not at all expected to be perfect :). Like anyone else they are individuals with strengths and weaknesses, and the current Dalai Lama is strong in this area.
With this example, it's understandable to think that a Dalai Lama has to have this level of understanding of Tibetan Buddhism (I don't know whether he is the most learned of all but certainly has a reputation of being very learned on the subject).
But a previous Dalai Lama, the sixth Dalai Lama, was a poet, who had many romances and his poetry is loved by Tibetans to this day, I'm told. Sort of the Tibetan "William Blake". From this you can see also that the Dalai Lama doesn't have to be a monk. He refused to receive full ordination and instead gave back his novice vows when it reached the point where he was expected to become a monk.
The short life and tragic death of the 6th ("playboy") Dalai Lama
And some of the poems attributed to him, translated into English
Stallion On A Frozen Lake: Love Songs Of The Sixth Dalai Lama
The sixth Dalai Lama died at a very young age, age 24.
So it's not necessary. And when asked whether he will have a successor, then the Dalai Lama says it is depends on the circumstances at the time of his death, and is up to the Tibetan people, and jokes that now, with a quite popular Dalai Lama, might be a good time to end this centuries long tradition, in case the next one is a "stupid Dalai Lama" who disgraces himself or herself :).
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