the seed created by Electrum has 128 bits of entropy which is as safe as private keys.
This also puts up a red flag, 128 bits of entropy. Why not just say 128 random bits or 128 bits of info. Why create another term.
It also seems it might be possible to create a database of seeds. If computing power increases and users increases. You might get a match. Always wary of when passwords are shortened.
128 bits/ 8 bits per byte is 16 bytes of information.
Of course you can create a database of seeds. You probably won't do that if you're looking for profit or else, you are probably crazy.
We have the word list here,
https://github.com/spesmilo/electrum/blob/a3b4409e6e8d1c510f53494ca068633ce03f0cc7/lib/wordlist/english.txt.
As you can see in the wordlist, there are 2048 words available to be assigned to one of the word in a 13 word seed.
If we assume that the seed is in English, there are 2048^13 possibilities for a seed. If you can bruteforce 1million of them in a second.
(2048^13)/1,000,000=1.115303726x10^37 seconds needed
=1.858395433X10^35 minutes
=3.097325722X10^33 hours
=1.290552384X10^32 days
=4.301841281X10^30 months
=1.178586652X10^28 years.
This is if you are bruteforcing without checking the network if the addresses had any transactions. Let me know when you find the rate where you can bruteforce a seed in a lifetime.