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It is reported that some people stored the seed phrase for wallets including bitcoin on lastpass. This appears to have allowed attackers to brute force the encryption and gain access to the keys.

My understanding is a seed phrase it designed to be a way to backup a number in the range 1 - 2^132 that is resistant to transcription errors. This makes it suitable for a backup strategy that involves writing it on a piece of paper. However it seems very far from optimal is one is storing it electronically, where there is no risk of transcription errors. In particular it looks like a seed phrase if someone come across it, but also the inefficiency of data storage makes brute force attacks much easier. Had these people stored the seed as a number rather than a sequence of words it seems likely they may not have lost their coins.

Why do people store the seed phrase electronically rather than just storing the integer?

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Perhaps because transcription errors are always possible if you are unwilling to trust an insecure network or insecure device to move the seed from, say, a secure offline device to a different place that is acceptably safe from fire, theft or accidental loss.

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