I'll start with what COSPAR wrote in 1964, emphasis mine:
COSPAR "accepts, as tentatively recommended interim objectives, a sterilization level such that the probability of a single viable organism aboard any spacecraft intended for planetary landing or atmospheric penetration would be less than $1\times10^{-4}$, and a probability limit for accidental planetary impact by unsterilized fly- by or orbiting spacecraft of $3\times10^{-5}$ or less."
The OP appears to think this $1\times10^{-4}$ probability is terribly loose. It's the opposite. It is terribly tight. It has its origins in the very start of NASA. In 1959, Abe Silverstein, NASA's director of Space Flight Programs, made the U.S. space agency's first formal statements about planetary protection:
The National Aeronautics and Space Administration has been considering the problem of sterilization of payloads that might impact a celestial body. ... As a result of the deliberations, it has been established as a NASA policy that payloads which might impact a celestial body must be sterilized before launching.
This early sterilization policy required NASA to bake the first five Ranger spacecraft in the pursuit of 100% sterilization. This baking almost certainly resulted in some of the failures of the early Ranger missions:
Ranger bore the brunt of the difficult constraint imposed by sterilization. Any spacecraft likely to land on the surface of the Moon or a planet, by accident or by intent, had to be free of Earth's pervasive microbial population. This scientifically imposed international requirement placed a tremendous burden on Ranger engineering and development, and greatly multiplied costs. Of course, it also took its toll on the useful life and reliability of sterilized components and is believed to have had a seriously degrading effect on early spacecraft performance.
As an aside, the stringent requirements for heat sterilization may have, in the long run, resulted in the development of more reliable hardware, in much the same way that insecticides cause insects to develop an evolutionary resistance. But early Ranger spacecraft had to pay the price of meeting these stringent requirements. While there never was any positive proof that sterilization caused difficulties with electronic gear in space, there were many reasons to believe this was a factor in the high initial failure rates.
In addition to the problems with those first Ranger missions, there was a set of planned missions in the early 1960s that presented challenges with regard to planetary protection. The US wanted to land humans on the surface of by the end of the 1960s. That goal represented payloads that would never be sterilized. I can't find a reference that states how COSPAR backtracked on its initial 1964 statement with regard to the Apollo project, but this almost certainly happened.
The only way to make the probability of a probe releasing Earth life on some other body be zero is not to go there. NASA realized this very early on. Even with the most stringent processes, anything sent from Earth to land on another body will have a non-zero chance of infecting that body with Earth life. The $1\times10^{-4}$ probability was set as a very high bar. As an example, with increased interest on Mars, COSPAR lowered the bar in 1969:
COSPAR "accepts as the basic objective for planetary quarantine of Mars and other planets deemed important for the investigation of extraterrestrial life, or precursors or remnants thereof, a probability of no more than $1\times10^{-3}$ that a planet will be contaminated during the period of biological exploration. The period of biological exploration is assumed to be 20 years ending in 1988, and the number of missions to or near the planets is assumed to be 100."
COSPAR has repeatedly lowered the bar to something more achievable. Here are the planetary protection requirements for NASA's most recent Mars mission:
At launch, the entire payload going to Mars (the Perseverance rover, Ingenuity Mars Helicopter, cruise stage, aeroshell, and descent stage) carried fewer than 500,000 bacterial spores (dormant forms of bacteria). This is a tiny number as far as spores go and wouldn’t even cover a typical smartphone camera lens. Of this number, the parts of the Mars 2020 spacecraft intended to land on Mars – including the rover, the parachute, and the descent stage – had no more than 300,000 spores in total. The rover itself was allowed to have just 41,000 spores, spread out over the vehicle’s entire surface area.
The $1\times10^{-4}$ objective for missions to Europa or Enceladus appears to be an unmodified version of the 1964 "tentatively recommended interim objectives". My prediction: If NASA is funded to send a mission to Europa or Enceladus, that unrealistic goal of a $1\times10^{-4}$ chance of infecting the body with Earth life will be changed to something that is achievable.