If I recall correctly the testimony was given and has been conveyed. The privilege no longer applies. Yes, It may take time. The longer it takes the closer the election gets. at some point Congressional Republicans will have to consider if they want to be caught out defending Trump when he does lose in court or when the really damaging info hits the fan. Some of them are not going to want to ride that one. as it is there are at least 3 Republicans who have said they plan to enter the primary. 2 of them have meaningful standing in the party, executive experience, and a very different view of the law than Trump. While they may not beat the party machinery they can argue that Trump is an awful choice to continue with by pointing out the damage he has done to the economy and international relations among other topics.
It was rather difficult when Nixon was there and it was the cover-up evidence that did for him, rather than the crimes under his watch. It took 15 months and the repeated exposure of executive malfeasance to drag Congress to the point of preparing to refer Impeachment articles to the Senate. Public opinion was widely divided and wildly manipulated. In the end the evidence was persuasive and Republicans did not want to defend Nixon in the face of it.
We have a very different set of forces today. However that doesn't mean it will not succeed. Nor does it mean he cannot be Impeached. The process could be long and ugly. The Ugly may work against the defendant in the long run. To some extent the law is clear and the Duty to Impeach is not something to ignore without consequence IMHO.