Explain to me why it's important to have a training plan

You don't.  It's a scam perpetuated by the coaching community to just raise their profits.

You go ahead and train however you feel.  Report back after a year.  Experiment of one, and all that crap.

But, gee, Scout, I see a lot of free plans out there. How does the coaching community profit from that?

I'm sure you'll get a lot of feedback about this.  All I'm going to say is that pre-training-plan days for me had me with overuse injuries and only progressing so far.  Since being on a training plan, put together by a certified coach who knows much much more of the scientific junk than I even want to know, I have been getting fitter, faster, stronger, healthier, & happier.  There's a lot to know out there and I don't necessarily want or have time to learn it all. I leave that up to those that make the training plans &/or the coaches.

 I'm sure there is nothing wrong for someone just going out and biking some, running some and swimming some, but I think once your training load increases and you get hooked on the sport and doing the best that you possibly can in it then a training plan doesn't hurt to help organize the workouts so you get the most bang out of each workout and stay healthy.

That's how they suck you in.  Like crack dealers on the corner.  First one's free.  After that, ya gotta pay.  Pretty soon, you see triathletes breaking into houses to steal from good, honest folk, just so they can feed their filthy habits. 

I'd say if you're going all-out during every workout "train as hard as you can in the time you have" you're probably going to wind up injured, overtrained, burnt-out, or all of the above. Plus your workouts will lack focus and the progressive build that is needed in order to see improvements over time. Your workouts will lack focus and you will not come close to being able to reach your potential.

x2

Isn't this, in effect, a training plan?  You have a plan for how you are going to train.  You are going to train as hard as you can, focusing on improving your weaknesses.

Sounds like a plan to me...... 

Pretty simple.  You may not choose to, but you will always get beat by someone who does ..........

Not being harsh, just stating reality.

Hence the reason people hire coaches who can then help them structure a plan that fits their lifestyle, or why people do tons of research on the topic and then develop their own plan ......

And every plan is broken down into meso and micro -cycles.  They are structured around clumps of workouts.  No one is all that important.  It is the combination of them all in a structured manner over longer periods.

Now we're getting somewhere....

You don't need to follow a daily structured plan.  In fact, the only reason Pfitzinger and Douglas did so in their book for marathoning was people demanded daily planning.  They were against it at first.

Having a basic structure to your training is important.  Following a daily routine may not be. 

Then it sounds like you are doing what's right for you....  I tried that for a while, then wanted to improve, and improve efficiently.  Meaning, getting the most "bang for the buck" out of my training time.  Like the other posts said, I realized that having micro cycles, base workouts, tempo workouts, LT workouts, interval workouts all planned out to train the body, helped me actually train more specifically, with less wasted time.  I thought it was more enjoyable as well.  A good plan mixes it up enough that I wasn't just repeating the same workout all the time.

Now, am I a slave to the plan?  NO.  I try to stick to it as best as I can, but If I am running short on time one day, I may move things around a bit.  This week, I did my brick yesterday because I only had time for that.  Then moved yesterday long bike to Sat.  If I'm tired, I will change a workout to a recovery workout.  I use plans as a very good outline to peak for a race - not the end-all-be-all gospel...

ditto on the injured and overtrained comment.  That's EXACTLY what happened to me.  Last year after I had my last baby, I came back quickly and trained hard.  I didn't follow a plan, didn't stretch, didn't do any strength training (core work specficially).  I just went out and swim/bike/run as much and as hard as I could whenever I could.  Now I'm paying for it with a bunch of over-use injuries that didn't surface until the end of the summer.  Six months later I'm still doing PT and have lost almost all my fitness (I can only swim, barely).  I had high hopes of doing my first Olympic Tri this summer and now I'll be very lucky if I can eek out a sprint. 

If I would have followed a basic (and even free!) training plan I have NO doubt I would not be in the miserable position I'm in today.  I made SO many mistakes last year.  When I heal and start training again, I'll totally do thing differently.   I'll stretch and do core religiously and I'll follow a training plan that is periodized. 

Learn from my mistakes.  Its not worth it.  Not at all.