EDIT: Thanks everyone for the information -- very interesting.
They cannot do other things just because "no law restricts it".
The exact authority grant is complicated.
You want:
https://www.law.cornell.edu/uscode/text/15/78d and following sections, plus a whole bunch of stuff enacted elsewhere.
The part you are probably most looking for is: https://www.law.cornell.edu/uscode/text/15/78u
There you can see most clearly their civil authority and what they are allowed to do. You can see it says "Whenever it shall appear to the Commission that any person is engaged ... in acts or practices constituting a violation of {a bunch of stuff} .. it may in its discretion bring an action ... to enjoin such acts or practices ... . The Commission may transmit such evidence as may be available concerning such acts or practices as may constitute a violation of any provision of this chapter or the rules or regulations thereunder to the Attorney General, who may, in his discretion, institute the necessary criminal proceedings under this chapter"
It then goes on to add additional monetary penalty authority that you see exercised here.
Random government authorities can't bring criminal proceedings anymore than the meter maid writing a parking ticket has the ability to haul you to court for parking in the wrong place. They send the information along to the people who do have that authority and act on it if they see fit (prosecutorial discretion).
The key words in the article are "civil, not criminal".
My keyword is why.
Separation of powers. The SEC is part of the executive branch. The judicial branch is responsible for bringing suit.
If you want the why for that why, that's a philosophical discussion that probably won't be well served by a HN comment thread.
Why would the SEC be able to imprison people? That's not their job. They also can't set the prime interest rate or grant radio spectrum rights to AT&T.
The concept of limited government demands that certain powers must be separated such that they never come together in the same person. That simple measure ensures that tyranny can arise only through conspiracy, cooperation, and collusion between multiple bad actors, rather than just one person acting alone. Why can't your HOA put you in jail for not mowing your lawn often enough? Because the kind of petty nagging nitpicking bastard that typically volunteers to serve on the HOA enforcement committee makes the absolute worst kind of cop. The power goes right to their heads, and they abuse the heck out of it to further their own goals and agenda.
The question we should be asking is why do the federal criminal investigators and prosecutors seem to pay less attention to financial crimes referred to them by the SEC than they attend to other crimes?
IF you are asking "Why hasn't the SEC been granted the power to send people to jail?", then that's a deeper philosophical question. There would be a concern that the diffusion of such powers could be abused or wielded by non-judicial-experts who aren't necessarily acting in the interests of justice and broader public policy, and more generally the principle of separation of powers discourages such to prevent tyranny/the abuse of state power.
Here is the law and reasons: https://www.justice.gov/usam/usam-9-27000-principles-federal...
Here are the statistics https://www.bjs.gov/index.cfm?ty=tp&tid=63
1) https://www.oas.org/juridico/mla/en/usa/en_usa-int-desc-guid...
I believe the Justice Department brings all federal criminal charges [1] under the Federal Rules of Criminal Procedure [2]. Bringing criminal charges is specialized work. It makes sense to have the specialists handle specialist work.
[1] https://www.justice.gov/usao/justice-101/steps-federal-crimi...