I think of it like this. Imagine if they tried to write Berlin in two syllables as 벨린. Because ㄹ is "L" at the end of a syllable and "R" at the beginning of a syllable, that would be transliterated as belrin which is kind of the opposite of what we want. So in order to get the r before the l we need to have that extra syllable in the middle.
Can anyone tell me how reliable the audios on here are? My hangul table tells me the '_' vowel sounds like the 'e' in the French word 'petite' which is an 'ö' like sound to me. But whenever I hear it pronounced here it sounds like an 'i'? Therefore 'Berlin' sounds like 'Perillin' to me not like 'Peröllin' ... I'm a little confused
I can't help with the vowel, but as for why the B-sound sounds like a P-sound, those two consonants are the same, but voiced and unvoiced respectively (meaning you engage your vocal cords on B, but not P, even though your mouth makes the same movements). For proof, try whispering "bat" and "pat" to yourself. Your mouth moves the same way, and the whispered words sound the same.
ㅂ has two sound b and p Mostly but not always: if ㅂ comes as a first letter, its sound is p and if it come in the middle of a word, its sound is b. I remind it's not a rule and it has exceptions. ㅍ: Sound of ㅍ is p, but the sound is like a p that the stress of a word is on that. You should say that with intensity. * Sorry if i have mistake in my English, my language is not English