Node's have rate limiting and will disconnect and refuse connections to and from peers that misbehave (i.e. they ban that node). So if a node sends a bunch of transactions too quickly, they will be disconnected and banned. If they send too many invalid transactions, they will be disconnected and banned. At worst, such an attack would take up a few seconds of CPU time before every node that this attacker has connected to disconnects and bans him.
Also, signature verification isn't all that slow. Nodes already fully validate every transaction they receive which includes signatures. In fact, it's faster to check an invalid signature because it will exit the signature check algorithm early.
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