As far as I read, the case with Cake wallet had to do with their random generator function, not with their way you'll import a seed. Besides the fact that it's closed-source, are there really any reasons not to import a seed phrase on another wallet?
Not all of the wallets function similarly. Different derivation paths, gap limit, possibility of various exploits being present in each of the wallets, etc. Using the same seed across different wallets can cause loads of confusion.
A downside of generating a seed phrase on a closed-source wallet is the RNG, but you can settle it by ensuring that the seed is generated by an open-source one with tested functionalities such as Electrum. Sure, there is a tiny possibility to get stolen from a wallet like Exodus, since you can't know if the wallet is operating maliciously, but I doubt if that will discourage someone from not making his life easier.
My personal opinion is to have two seed phrases. One for open-source tested wallets and one for the closed-source. That's for those who want to keep their seeds separated and not on a notebook. If you keep them on a notebook or anywhere else organized, you should simply write the software name next to the seed phrase to differentiate them.
Also possibility for certain codes in the program to leak your private key, intentionally or not. An example would be the Android Wallet exploit back in 2013 which had reused r values in their signature. You are increasing the risk of this happening if you were to use the same seeds across different wallets. I would not expose my seeds to different wallets unless necessary and would segregate them as far as possible. Besides, I personally don't have any scenario where I need multiple wallets, much less having to use a close sourced wallet.
And yes I have no doubt Electrum is safer since it is 100% open source. I heard Exodus still keeps some open source part. What I do not trust at all are some apps/extensions you can install on top of Exodus, made for stacking, investing and even gambling.
Consider sweeping your funds to a new Electrum seed when the funds are low or when you're sending a new transaction (send the change to your new Electrum wallet). Electrum's seed system is much easier and unambiguous as compared to the BIP39 that other wallet uses.
