What is your advice on re-enlisting as an 11X? Should I take it or leave it?

Typically when the little voice whispers at you, you should strongly consider its advise. If you dont enjoy PT or pushing yourself to new extremes then 11 series may not he for you, and that's okay. If you dont like pushing yourself you can still be Infantry, but you will never excel.
There are a metric ton of options that dont involve Infantry. Just because the money is big doesnt mean you should do it. You might get $40,000 to blow on strippers, but if you hate your job is it really worth it?
As for the Infantry in combat question, a conflict can kick off at anytime that will require boots on the ground. Training will always be centered around where we think shit will hit the fan next. I went 13 years without going into a gas chamber, North Korea made that happen again.
Good luck.

So what do you want to do with your life? You need to figure this out first. Your old job, working with Patriot system, looks challenging. I've seen infantry, specifically airborne infantry, from the outside. Mostly the junior enlisted appear to be dedicated and highly motivated to accomplish the mission. They willingly boarded the aircraft in an orderly way and then either jumped out (insane to me, but I was the pilot) or off loaded on the ground in an orderly and safe manner. The physical demands appeared to be high. When dressed for deployment into a hostile area they carried a heavy load of equipment. Good because the Army obviously provided them the stuff they needed to do the mission. Bad because it weighed a lot! Long term, I see potential injury to knees, hips, and back.
Here's my bottom line: look at your options. Pick the one that most closely matches your personal goals in life. Infantry can be a rewarding career. If you're looking for a job that is readily transferable to the civilian world, then avoid Combat Arms. Logistics jobs from Log Planner to Engineer, to truck driver are much more readily transferable to the civilian world. Same for the Signal Corps with communications and IT MOS.

When I was active my PMOS was 19D (Scout) and I had a SMOS of 11B (Infantryman), both were earned with my boots on the ground and I can tell you - If you aren't ready for either then you need to save everyone the trouble and go back to what you do best.
There will be no pillow talk at that school.

I quote an online comment: "When you visit the local Army recruiter and you KNOW you want to become an Infantryman, you will be given the 11X enlistment option. Unlike other Army career tracks, MOS 11X isn't a military occupational specialty (MOS). The Army does not offer a guaranteed job for any specific infantry MOS; the "X" means that the specific job is not known at the time of enlistment. You must earn a slot to the infantry during your training. Individuals who enlist under the 11X Infantry option attend Infantry OSUT (One Station Unit Training), which combines Army Basic Training and Infantry AIT (Advanced Individual Training), all in one 14-week course. During the training, recruits are allowed to list their specific infantry job preferences, but ultimate assignments are determined by the needs of the Army at the time. This training is held in Fort Benning, Georgia."

Let's start this off with things they don't tell you going 11B aka 11x . This is based off of my experience 25 years ago ,but I imagine it hasn't changed much. Can you max out a P.T. test? I could max out pushup and set ups but never could run. 14:10 was the best time on the 2mile run this eliminated me from any schools (airborne or ranger). I might mention I did pass the ranger swim test , but since my run time was bad they never sent me to RIP. Do like being out in the field 28 days and no shower. Canteen baths only. US Army standard of being able to carry a 60 pound ruck 25 miles. My ruck never weighed less than 120 and since I was a 60 gunner another 20 for my weapon. We had 25 mile marched every 3 to 4 months. A 12 mile every month with full gear. Now don't get me wrong I loved being 11B , but if I was to go back and tell my younger self something I would say go for a job that you can do in the civilian sector once you get out. Not to mention the white , blue , red and black cycles. The cycles that determine if you are first to go to war. One of they cycles you do nothing but details around post like mow yards or pull gaurd. And one you can't leave post because you are first to go. I hope this helps you in your decision.

Take it

Even snipers have to be fit

You better get fit.

Stick with the 14...

are you coming back in for the purpose of retiring or just a "few more years." Is 11X going to get you to where you want to be in 5 years, 10 years? Examine where you see yourself professionally in the next few years and weigh that vision with the MOS you choose. good luck

Ignore your Supervisor and listen to what you think. It is you that will regret never trying it or it will be you regretting have tried it. Honestly, I thought Infantry was fairly easy vs being hard core. Yes it is more physical than other MOS but the level of being physical is not like being on a sports team or anything and it is fairly easy to maintain the level of fitness required without even going to the gym (I managed it for three years). You will have to run sometimes on your free time because some Infantry units slack off now and then on PT (going to the field and field recovery are prime examples). As for going into combat or not, you shouldn't enlist in the Army in the first place if you want to avoid combat. I don't know who your kidding there. MOS 14T, (Patriot battery) is almost number 1 on the OPFOR airstrike list if we go to war with China or Russia. Not every war is a light insurgency. In fact with the sanctions and trade frictions I would rate a future war with Russia or China as extremely likely.