BIP39 algorithm is open source (is known) and pretty straight forward so it is very easy to implement. This means there isn't a need for a special software written by some super expert programmer to be used. If you know basic programming you can write a tiny script that performs what's needed in BIP39 to convert your seed phrase to a private key.
Nonetheless, people shouldn't be expected to write their own recovery software, no matter how simple it might be. That's recipe for disaster.
Some people may hate me after I say this, but Bitcoin Core isn't a very newbie-friendly bitcoin wallet. BIP39 has been around for a decade, and they could have added support for it. The developers either don't want to, don't see a great need for it, or there aren't enough requests to add it.
Neither of the three. According to this reply from Bitcoin Core developer achow101, it is not considered "safe enough":
BIP 39 is not in Bitcoin Core largely for implementation reasons and because BIP 39 is not as secure as it could be.
The structure of Bitcoin Core's wallet doesn't really allow for BIP 39 to be implemented. The current structure doesn't allow for 512 bit seeds as BIP 39 specifies, and adding it would require some significant changes to the wallet code. Implementing BIP 39 would also require implementation of PBKDF2, although that isn't very hard.
Also, more generally, many Bitcoin Core contributors don't consider BIP 39 to be secure. It uses PBKDF2 which is generally regarded to be a fairly weak KDF so it isn't considered to be good for the secure storage of all of your Bitcoin. Some software (such as Electrum) used BIP 39 in the past but have switched to using their own mnemonic algorithm because of this weakness in BIP 39.
BIP 39 mnemonics have some other issues as well such as version numbering (or rather lack of) and the use of a fixed wordlist. Electrum has documented their reasons for why they don't support BIP 39, and those reasons are the same for Bitcoin Core.
That does not explain why they haven't come up with a similar, more secure standard like Electrum, though.