TSP was created to be a retirement plan for Federal government workers, which is why it only allows participation by Federal government workers (and dependents and survivors). Yes, it is very like a 401k; it was designed to be modelled almost exactly on the already-existing 401k program, except that 401k's can only be sponsored by a private entity which the government isn't, so they created a new section of law that basically copies the law for 401k's except making it for the government. This was done essentially for the same reason that private businesses supported the creation of defined-contribution 401k's and migrated to them in droves -- it transfers the long-term investment risk from the employer to the employee, and makes the employer's balance sheet look better -- benefits(?) the government wanted to share.
TSP is NOT itself government backed. The G fund invests in Treasury bonds, which are government backed, but in any IRA, and at least most 401k's, you can buy a Treasury and/or 'agency' bond fund with the same backing. The other TSP funds are market index funds exposed to just as much -- or little -- risk as market index funds you can buy. TSP and its funds do have low expenses due to economy of scale, lower than many probably most 401k's, but you can find roughly as low expense IRA custodians and index funds with a little effort. You may not easily find zero-overhead lifecycle/target funds, but if not you can get the same result by adjusting your investment allocation every few years, not a terrible burden.
(In contrast, the CSRS FERS or military pension is a traditional defined-benefit plan, which is guaranteed by the government, and must be actuarially funded and reported as a liability.)
There have been proposals from time to time to open TSP to people who do not have a satisfactory plan from their employer, for somebody's definition of satisfactory. Analogously, PPACA/'Obamacare' attempted to provide medical coverage to people who don't have 'minimum essential' coverage from an employer, partly through Medicaid/CHIP and partly through competing private providers. As with PPACA, one criticism is that employers who now provide a plan that may be a little better than the minimum will drop it because they can argue the government backstop is good enough. Several states recently have created or are creating state-run backstop IRA schemes, and experience with them may -- or may not -- help promote a Federal move.