If I've heard it once I've heard it a hundred time; "But I have to go Rx, see, 'cause if I don't it means I'm less of a human being. I have no value as an athlete and my friends/relatives/classmates/significant other won't love/respect/be awed by/adore me any more. I'll die from shame".
That's not what you said. What you said was "C'mon, coach, I can do it". What I heard was what you meant, the words in your head. And your heart.
There's a lot that goes into the decision to go "as prescribed" and if we're going to talk about it we have to understand some things.
What Rx means
Back in the dark days before the revolution prescribed weights, reps and rounds were the way to develop a common language. A marker of performance. Rx has always been a measure of fitness of upper-intermediate to lower-advanced level athletes. (Generally, this is about a two year development.) Even back then, if you were new or not ready for those loads or volume you scaled so you would get the intended stimulus from the workout, i.e. what the super smart programmer meant for you to get out of the workout. Rx was never meant to mean "at all costs". Unfortunately, due to this thing called ego, it quickly came to mean "you gotta". Doesn't matter what your reps look like, put yourself in danger of injury if that what it takes, "Rx" is all that matters.
That ain't it, kid. Rx is simply a way of benchmarking your current fitness and a goal to be worked for. The loads have only gotten heavier, the workouts longer and more complex, making it even harder to keep perspective. If you've done this for any length of time you remember when "Diane" (21,15,9 Deadlift 225#/ HSPU's) was a heavy deadlift and, for most of us, an impossible bodyweight movement. Now it looks kind of quaint. (Quaint, as in, hard, fast, classic CrossFit couplet.) Dan Bailey did it in 1:35 at Regionals. But he's Dan Bailey.
What Rx Is
Rx is a standard. Immutable, permanent, unwavering. If you are not externally modifying (banding, etc.) your pull ups, for example, yet are keeping your arms bent at the bottom and/or only going nose over the bar you are not doing the workout Rx. You are violating the standard and therefore are not "going Rx". This also includes whatever physical limitations you have. If you're incapable, for whatever reason, of getting below parallel in your squat, I'm sorry, you're modifying the movement and not performing the workout as prescribed. Are you doing your best? Of course. Is it unfair? Absolutely not. Modifying to be able to perform the movement isn't a sin, it doesn't make you a bad person, it's simply the way you have to modify that particular thing. And you don't write "Rx" on the board or in your journal.
What Rx isn't
This is simple. Rx isn't using the prescribed loads, rounds and reps and turning in a time 3 times longer than the workout is designed for. Fran is a 4-6 minute workout. If you're doing Fran in 8 minutes you're not doing Fran. Are you working hard? Are you burning a bunch of energy and eating a lot of chalk? Sure, but you aren't doing Fran. And you are not advancing your fitness as much as you would if you modified and went faster.
Ditto for AMRAP's. If a workout is designed for an upper-intermediate level athlete to get 6 rounds and you get 2 you (and your coach) have messed up. Bad.
Every workout has a stimulus baked into it. Helen, Murph, Cindy and the rest all have a very specific purpose. Do that workout, accomplish that purpose = make progress. Simple.
How to get there
Baby steps, Bob. Rome wasn't burned in a day. As a very smart Dan John says, "the goal is to keep the goal the goal." Whether that goal is health, fitness and longevity or the podium at the Games you have to approach your workouts with some kind of plan. That plan needs to include excellent technique (don't hurt yourself), reasonable volume (don't hurt yourself) and a proper level of intensity (don't hurt yourself). All goals, whatever they are, have to have these 3 complementary components. Have to. You won't get very far without them.
Start, always, with great Technique. Watch people who are really good at what they do. The Rich Froning's and Annie Thorisdottir's of the top 10. Ignore the other 99.44% of what you see (especially on YouTube). In competition the exceptional ones (i.e. the ones you want to emulate) look like they're barely moving and yet they win. Why? Because they're very good (read: well practiced, smooth, level headed, smart, under control, emotionally stable). These people are your benchmarks.
Next up, reasonable volume. Let your coach scale you back so you finish inside the time or round window. This is where you build Consistency. Every rep should look the same with no or little degradation. Fatigue ruins consistency. Don't let it happen.
Now we can ratchet up the the Intensity. Push your good technique and higher volume for a faster time or extra round. Now that makes sense. Pushing yourself through too many crappy looking reps is the path to being "that guy." Practice sloppy and/or slow and guess what you get? You're better than that.
This process takes time. It'll come in bits and pieces, a movement here, a workout there, as we get better at the oh, so many movements that make CrossFit what it is. Be patient, revel in your small victories and improvements. Patience not your thing? Then sign up for some Private Coaching. Your coach can tailor movements and progressions that will make you better faster. But, in the end, there are no shortcuts. Make haste, slowly. Rx is a goal but you can't jump over the journey.