JBOK (just a bunch of keys) wallets generate the keys independently from each other.

In contrast, HD wallets are hierarchical and deterministic: They need a seed (e.g. a couple of words) and can generate the keys with that. This allows HD wallets to have a convenient backup mechanism: Just store the seed (e.g. 12 words with Trezor Model T, 25 words as with Trezor Model One, 24 words, 12/24 words with Exodus, 12 words for coinbase, 12 word for Electrum). I'm uncertain if any of those wallets use it, but the procedure is described in BIP 32 / BIP 39 / BIP 44.

Every single wallet I've checked is a HD wallet. Do JBOK wallets (still) exist? Do they have advantages over HD wallets?

For example, I could imagine that JBOK wallets are more secure because they are simpler. Are there any known issues that come from the way the keys were derived / errors in the implementation?

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All wallet software that I know of has migrated from JBOK to some form of deterministically derived keys. The first wallet with deterministic key derivation that I know was Armory around 2011-2012, and its scheme inspired BIP32, which formed the basis of many key generation standards that followed. Obviously, software that predates these schemes did use JBOK (in particular, the Bitcoin reference software did, before it was called Bitcoin Core). These days Bitcoin Core still supports JBOK wallets (e.g. if you load a wallet created by an old version), but new wallets by default are BIP32 based.

As far as advantages goes, I know of one: JBOK wallets "unsteal" themselves over time. If someone finds your wallet file with keys, they have access to your current funds, and a number of future keys that are typically included in the backup. But over time, as you create more receive addresses and transact, moving old coins to new change addresses, these coins become out of reach for an attacker.

It's a small advantage only, and presumably not considered important enough to weight up against the advantages of easier backups.

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