It doesn't, precisely because of that. As for the reason (take this all with a grain of salt, I'm no expert by any means) -- it takes computational power to verify the transactions via the blockchain, and there's only so much computational power/time available. Therefore there's a 'reward' you set up for whoever processes your transaction. In time, as the blockchain got more congested, people were willing to offer more/it cost more to send things. Think of it like a toll-booth where you're semi-allowed to choose what you're paying; if it's busy, you'll pay more, otherwise you won't get through. Eventually people start paying ridiculous amounts just to get through.
And it's not really a currency precisely because of that, and the loooong times it takes to send money. Add to that the volatility, and it's more like you've got a really weird asset that people say is a currency.
edit: this is what people predicted with bitcoin happening, which is why some alternative coins have taken off - some of them tackled these issues and are prepared for scaling issues.
Many thanks for the explanation! I think I need to do a deep-dive on cryptocurrencies soon...
No problem! I think it's well worth remembering that, as is always the case (but maybe moreso with this subject), people who are invested can be quite evangelising and won't mention downsides themselves. Take everything you see with a grain of salt, and it's worth actively looking for dissenting opinions.