No, bitcoin is not going to take over the role of Remittances or even disrupt it. Bitcoiners are always trying hard to place bitcoin in a competition with fiat by always suggesting that it may likely take over the traditional system. Bitcoin is just an alternative, the both of them are going to co exist side by side for people to choose their preferred cross border transfer option. As for bitcoin, those who care so much about privacy and decentralization would stick to it.
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i agree with what you said that bitcoin can coexist with the payment system that people usually use... it can be used as an alternative payment for people who like a decentralized and secure transaction system. although in its use there are several obstacles such as volatility, difficulties for laypeople, etc., but bitcoin offers cheaper, faster, and censorship-free transactions, allowing people to make transactions without problems compared to traditional methods.