I'd like to know whether any deep reason exists why conjugations for ich and er,sie,es are the same.
Most of the modal verbs are so-called preterite-presents (Präteritopräsentien). A demonstrative example is the German verb wissen (though commonly not counted as modal). "Regular" verbs have an -e ending in the first person singular present and a -t ending in the third person singular present.
ich gehe, er geht.
However, the verb wissen has
ich weiß, er weiß
without the expected endings. The reason for this is that once the current present forms of wissen were past forms. You might know that in past tense of strong verbs, the first person und third person singular have no endings; e.g. in
ich ging, er ging.
So the current present tense of the preterite-presents were past tense forms in Indo-European or early Germanic times.
Coming back to the verb wissen, we can notice that this German verb is related to the latin verb videre, to see. So ich weiß once had the meaning of ich sah/habe gesehen. If you have seen something, then you know it. So it was possible for the past tense form to gain a present tense meaning.
Most of the other modal verbs have a similar history with a tense shift.
Additionally, you might notice that the modal verbs of the English language take no -s in the present tense third person singular (he can, not he cans). The reason for this is the same: These present tense forms once were past tense forms.
I have simplified things here: I have treated current forms like ich weiß as if they were the forms as found in older stages of languages. That's of course not true, but there have been several sound changes. However, these sound changes were regular so that the first person and third person forms evolved parallelly to yield ich weiß and er weiß.