No, with a 12 int and proficiency I can't do stuff, because the wizard, the artificer... with +3 int already have the same bonus for nature/religion without proficiency as a proficient character with only 12 int. But that's also a problem of the proficiency bonus itself, it is so low that it simply does not matter enough.

In one of my games we found a Headband of Intellect last session, we're at level 3 and I play a bladesinger wizard with 16 int (and 20 dex, 16 con, rolled stats), and I gave the Headband to our cleric, who is really glad that he finally can play his character like he always wanted to - actually knowing about his religion, his faith. Being a heavily armored Tempest cleric, he needs all three of con, str and wis to be good, so even with his fairly good rolled stats, he only had like 12 int before.