One reason not to have a voter turnout threshold is that generating interest on non-controversial issues can be hard.
For example, suppose that there is 98% support for a measure to remove the king from the constitution of a nation after the king abdicates his throne with no successor in place. But, since it is uncontroversial, only 10% of the population votes. If there was a higher than 10% threshold, this uncontroversial measure might not pass, even though all proper processes were followed.
Another possibility is that most people don't care, even though some do.
For example, suppose that there is a measure to determine if the nation should transfer a small, uninhabited island to another nation, and 90% of the population doesn't care, but 10% of the population is hotly divided and cares a lot. A referendum allows the decision to be made in a manner that doesn't taint the eyes of sitting politicians for the 10% of the population that cares a lot in a definitive way that may require a referendum for constitutional reasons. A threshold leaves an issue of importance for some purposes unresolved.
More generally, referendums are usually held because some issue needs at definitive resolution that, for whatever reason, ordinary measures don't resolve. Often getting a definitive resolution is more important then how it is resolved. A threshold requirement thwarts this purpose.
A third possibility is to discourage the political tactic of a referendum boycott.
A threshold allows opponents of a measure that has majority support among people who would usually vote into a defeat, by not voting at all, rather than showing up and voting against a measure, in a country where voter turnout isn't all that high relative to the threshold.
Suppose that the threshold is 30% and typical voter turnout is 40%. If 25% of people support a measure, 15% of people oppose it, and 60% of people aren't bothered to vote, the opponents can win by boycotting even though they couldn't win by voting. And, you generally want to design a system in which the incentive in the political system is to participate, rather than to boycott, an election.
The last problem could be cured with a threshold of affirmative votes for the measure only, rather than a threshold of total votes, and a requirement that a majority of votes cast support the measure. This is a system that is used in the U.S. in many elections of workers on the question of whether a workplace should be unionized.
For example, if the threshold is 25% of eligible voters voting in favor, and a majority of the votes cast also being in favor, boycotting won't work, but decisions of importance can't be made via referendums unless there is a decent affirmative base of support for the measure.