I think the end result is, get one good custom profile for each printer/paper combination so the printer & paper are being used to it's fullest and most accurate capability in that part of the printing path, choose which RI works best for the image and know generally what mapping each RI applies, and make the rest of the adjustments intentionally in LR/PS.
Accurate capability is a big rabbit hole without actual data.
What we have here are three very different attributes of color: accurate color, matching color, and pleasing color.
Let's start with accurate color since you originally brought it up. Like gauging anything for accuracy; speed, distance, height, weight, we need to measure something and compare it to a
reference to know if it's accurate. This is true for color. Let's say you show me two images on-screen of a red apple. The color of each apple is noticeably different. You ask me "
which is the accurate color of the apple?" I can guess but I cannot answer it accurately without measuring the apple with an instrument designed for that task. A Spectrophotometer will provide device-independent numbers of the color, a value in Lab. I then need to measure the exact same spot** on the display for both apples and produce that Lab value for each. Now I can use a formula (they differ too) to calculate the distance/difference in the actual apple and the two images of an apple. If the value is greater than 1.0, it is said to exceed JND (Just Noticeable Difference). IOW, if the image on the screen and the apple are a detlaE (dE) of 1 or less, they appear the same to the observer. This isn't going to happen but the idea is, 1.0 or greater is a visible difference, higher, more difference. Less accurate between measured color and resulting color.
Moving to another kind of accuracy; measurement of distance. Let's say I measure my foot with a ruler and find it's 10.7 inches. Clearly, my foot isn't an adequate measuring device compared to a 1-foot wooden ruler. But how accurate is the ruler? It too should be of sufficient accuracy for the task. There are devices like a 50 cent wooden ruler that may be accurate to +/- 1/10 of an inch. For measuring a 40-foot wall, that may be all that's needed. For measuring a component that will be used on a spaceship, 1/10000 of an inch may just be adequate. But my foot clearly isn't. So when we talk accuracy, we need to take into account the instrument or method of measuring the accuracy. And how accurate we need the results of the measurement to the reference. With dE, 1 or less is invisible. There's a difference but for viewing a solid color, it's moot.
Color matching may have nothing to do with accurate color due to metamerism (which is good and provides a visual match) and metameric failure where we don't get a match but might have the ideal color 'accurate' values.
Pleasing Color is subjective and has little to nothing to do with any of the above. Back to Color Appearance vs. Perception.
**Getting back to color in context, viewing an entire object, print, display: An apple isn't a single color! So I'd have to measure many spots on the apple as well as the screen. Digital images are composed of thousands or tens of thousands/millions of solid colors. As would our apple. Zoom out of the image on-screen, it appears like an apple. Zoom in, it's just a big pile of solid color squares with color numbers. As you can see, discussing the accuracy of a photo of an apple and the apple itself is a big job!