You are overthinking this. There's nothing new or unusual about the definition 'To advance toward the speaker or toward a specified place; approach'. This is a straightforward and literal use of a common verb and a common preposition. It's not idiomatic at all. And yes, it's certainly common and natural to use 'come to' in the sense of 'approach' because that's what the verb 'come' and the preposition 'to' mean - a movement towards the speaker. For example, a helpful boss might say to a new employee, 'If you have any problems, just come to me.' The use of 'come to' someone meaning to 'occur to' is more figurative, but the concept is similar. For example, 'An idea suddenly came to me.'

Yes, both uses are common and natural. Bob