You bring up defamation laws as alternatives, so that financially injured individuals could sue and be compensated.

You should realise that would still be a restriction on free speech. The government would act as arbiter (court) and last line of enforcer for the financial compensation. The court would therefore be involved in the restriction of speech.

You may be arguing for a far less restricted free speech than currently by moving it out of the realm of criminal law but by saying civil law would still hold jurisdiction over speech you're not arguing for a completely absolute free speech.

to expand with an example. In sweden there isn't any law for defamation against companies (so called "economic defamation"). Physical persons can sue each other for defamation but legal persons can't.

Swedes would therefore say that their free speech is less limited (closer to "absolute") than the americal legal framework since swedes can say what they want about companies without having to worry about any government interference while americans can't since the matter can be brought to court and enforced by the state.

"Absolute free speech" as a concept requires not only a removal of criminal restraints but any form of restraint which the government enforces, of which civil law is an example. For free speech to be absolute not only would criminal laws have to be removed but also civil legal responsibility.