Let's state a few facts establishing the preconditions:
The GOP and their senators, by and large, have made their peace with Trump's presidency. They do not want him removed from office, neither by election nor by impeachment.
Tolerating this President involves tolerating a person very different from the conservative ideal and tolerating policies, especially budget policies, very different from central conservative tenets. It seems unlikely that the Ukraine affair is the straw that breaks the camel's back.
The only threat to the Republican senators are elections; for these it is crucial to not alienate the public.
To keep Trump in power, they must prevent the Ukraine affair from appearing sufficient for an impeachment in the public eye. To keep themselves in power, they must do so without creating the impression of a cover-up.
The goal of the GOP is emphatically not to "do a good job", as you phrased it, by conducting a meaningful investigation.
The Democrats' goal is about the opposite: They want to remove the president to begin with and don't tolerate the Ukraine affair. In order to sway the needed number of centrist Republican senators they try to build public pressure.
This lack of interest in the investigation by the GOP vs. the opposite Democratic interest results in a power game over the impeachment procedures.
Any evidence, every witness, every meme on prime time television threatens to influence the public, and the GOP tries to prevent these without losing credibility. The best thing that can happen is a boring procedure full of rituals, decorum and tradition at 1 a.m. that nobody who isn't on meth can follow without falling asleep. Its lack of substance is shrouded in its outer form: That of an important, substantial trial. That is what the public sees, and that is by design.
As an example, Trump didn't want "to drag [the House Managers' presentation] out through Saturday, ending the first week — and heading into the Sunday talk shows — with no formal response from the president’s defenders".
The schedule is informed by the necessities of TV, not by any necessities of investigation.
The GOP was concerned about keeping substance out of the public discourse to the extent possible without betraying this very goal.