Out of more than 1,100 unsolved murders from the Troubles re-opened by a team of detectives, it has emerged just one has been put forward for prosecution.
A Northern Ireland Affairs Committee report said the high cost of inquiries into Northern Ireland's troubled past is "financially unsustainable".
The NI Affairs Committee said the huge bill for inquiries, investigations and inquests is undermining the ability of the police to deal with current crimes.
It said too much focus on cold cases is compromising the police's ability to cope with present-day terror threats.
It said the Assembly should decide if there are any future inquiries.
The £34m project re-examining more than 3,200 killings needs reviewed, it said.
It was also revealed that the cost of the Saville inquiry into the events of Blooody Sunday is now £188m.
In its Policing the Past report, the Committee warned the cost of the Historical Enquiries Team (HET) and associated investigations could spiral to more than £45m - 60% over the original budget.
The estimated cost of ongoing inquiries and investigations during the next financial year is £100m.
Committee chairman Sir Patrick Cormack said: "The Police Service of Northern Ireland faces significant demands in terms of its work with all of the different historical investigations and we are concerned about the impact of this in relation to the police service's primary role in policing the present."
The unanimous view of the committee, which includes MPs from the DUP, SDLP and Ulster Unionists, was that those costs are unsustainable.
Ombudsman's workload
The SDLP's Alasdair McDonnell said allegations of wrong-doing by the security forces must be investigated, but does not believe inquiries are the answer.
The report also found the efficiency of the Police Ombudsman has been damaged by the workload posed by its remit to investigate historic events.
"I don't see a lot of demand in the future for further inquiries because I think the public are beginning to be concerned about the substantial amount of money in these inquiries that can go to lawyers and others, but with no direct benefit to the victims or their families," he said.
In future, the committee said the Assembly should decide if there are any further inquiries with cross-party support required
Cases dealt with by the HET that involve potential misconduct by officers in what was then the Royal Ulster Constabulary are referred to Police Ombudsman Al Hutchinson.
So far the HET has passed 54 investigations to the Ombudsman's office, with 300 more expected before 2013 when the chronological re-examination of files is due to be completed.
The report said: "The number of complaints about the former Royal Ulster Constabulary arising from the years of the Troubles and the inadequate provision of additional resources have compromised the Ombudsman's ability to investigate complaints against the PSNI.
"There is a risk that this reduced capability will damage public perception of the Ombudsman's Office and public confidence in policing."
The committee also said issues had to be resolved around PSNI cooperation with inquiries and unheard coroner's cases into killings during the Troubles.
It said the future of the HET project would ultimately have to be reassessed in the context of the findings of the Consultative Group on the Past.
Set up to look at how to deal with the legacy of the Troubles, the group is co-chaired by former Church of Ireland primate Lord Eames and ex-Policing Board vice chairman Denis Bradley.
It is due to present its recommendations to the government later this summer.
