First of all not only does the executive provide a check via a pink slip, the statute goes to the trouble to explain the standard to be applied. 'For Cause' does not mean no check exists through the conventional executive structure, it means that such a check does exist but that it is not broadly discretionary - other words not at the mere whim or fancy of Mr. President.
Other checks depend on the nature of the power used by the agency. There are multiple checks to ensure budgetary transparency and oversight
https://democracyjournal.org/briefing-book/why-the-cfpb-is-constitutional/
"And there are many other ways the agency is held accountable: unlike other bank regulators, it is subject to a statutorily imposed budget cap; it must undergo Government Accountability Office audits and Federal Reserve Board Inspector General oversight; it is subject to the strictures of the Administrative Procedures Act; by statute it must use cost-benefit analysis; and, as with other agencies, the bureau’s actions are reviewable by the courts."
As for overreach in regulation or application , the statute provides an alternative check using the Financial Stability Oversight Council which can override any decision by the CFPB. Now lets learn more about this council providing the needed policy and enforcement check that the President does not.
https://en.wikipedia.org/wiki/Financial_Stability_Oversight_Council
"The Financial Stability Oversight Council has ten voting members:[24]
Secretary of the Treasury (chairs the Council)
Chairman of the Federal Reserve
Comptroller of the Currency
Director of the Consumer Financial Protection Bureau
Chairman of the U.S. Securities and Exchange Commission
Chairman of the Federal Deposit Insurance Corporation
Chairman of the Commodity Futures Trading Commission
Director of the Federal Housing Finance Agency
the Chairman of the National Credit Union Administration Board
an independent member (with insurance expertise), appointed by the President"
Now pay attention to who appoints most of those members to their jobs and gives them their marching orders. Why its Mr. President!
Nothing it the statute protects this agency for the reach of federal courts and in a lawsuit happy Washington, you can already see the impacts of that check.
Congress has not been bashful either. There have been extensive hearings since the agency's inception and clearly an agency they molded, can be remolded with a bill in the hopper and a few votes.
Congress has a history of trying unconventional structures in regulatory agencies over the years to provide less direct but nevertheless effective oversight. They are entitled to do just that.