General rule of thumb is to have at least one day of rest to achieve maximum gains. There is no reason that you cannot train 7 days if the intensity is kept at a level where you are not aching too heavily, but you will pay a price in progress.

Based on your post you want growth and that requires you to follow the hit it hard, hit it fast, leave it alone system if you want the best. You will be doing a good deal of mobility and stretching which reduces the aching by allowing the muscles to flush out damaged tissue in the blood more effectively. There are two ways of viewing this, the most common is to accept the lower level of aching with gratitude, mine is to train all the harder to ensure I still ache ridiculously, I’m not always too bright.

Hit it hard. Growth is the bodies response to damage, if it realises it need to build more muscle tissue to cope with daily demands it does so. As such you have to hit the muscles hard to cause maximum controlled damage to the muscle fibres promoting growth. Rep ranges are ideally 10 down to 6 at rep max, so you should finish a set of 10 knowing there could be no 11th rep.

Hit it fast. You want damage but not so much your body won’t recover sensibly. You also need to be working at the higher intensity levels so shouldn’t be trying to draw this out. If you can work at 90% of your max with rests in a 30 minute session, great, if extending this to 45 minutes means you have to drop to 75% you have short changed yourself.

Leave it alone. The most psychologically difficult part of training, one everyone gets wrong on occasion. Your mind tells you that if you aren’t training you should be, your mind is wrong. Training causes damage, the body needs to repair this and will want to grow to avoid future damage, but if won’t be able to do this if it is still repairing damage. The arms are the most common area to have this and your session looks like it could be suffering this in the most common way. Bench press, shoulder press, all other upper body presses have the prime mover of tricep, lat pulls, chins, rowing etc. all have bicep as prime mover. Doing these will mean the arms are having to recover and repair, hitting arms a few days later. Your split has 4 days of arm work and 2 with leg work, something you will want to address.

Obviously you need a mix of strength and endurance for your sport otherwise you encounter some infuriating so and so like me who just blocks and dodges your shots until you tire then uses you for precision target practice. As such my present style of training might be a good one for you to try, strength circuits, with target of no rest and actual absolute minimal recovery to incorporate endurance.
Example would be my squat circuit session 10 reps a set using weight I could do 15 if getting rests
Squats at 100kg
Barbell calf raises 100kg
Goblet squat 32kg on bosu (the on bosu is not recommended if you are sane)
Touch floor tuck jumps
First circuit is not too difficult and I always grab a quick swig of water before starting squats again, break of a couple of seconds above time it takes to get into position.
By the time you have done three circuits the body starts to have a bit of a whinge about feeling tired and not wanting to keep going. So far I have managed to get up to 5 circuits and in fairness I had to take a 10 second break at the end of 4 to get my breathing back under control.
These aren’t long sessions but trust me it is tough.

Variation. I change sessions every 8 weeks, this can be changing style, exercises or some of both. Keeping the same routine for too long allows the body to get complacent and stalls progress, commonly known as hitting a plateau. For most the ideal switch time is between 6 and 8 weeks, for me it is 8.

I would say based on what you have said, you are too used to your training and being very moderate. This is safe and fine if happy to simply maintain with slow improvement, if you want more you will have to up the intensity and leave the comfort zone behind. This will force you to take more rest and you will progress faster. Balance issues on your weight training and errors you are making are incredibly common and a lot more minor than most coming here. You are getting in a good mix of cardio, mobility and resistance training which is very rare to newcomers here, congratulate yourself on that and keep to it.

I have not give a direct program I thought it could be useful to see what you think of this first. I would also need to know what kit you have available to you and what your priorities are. It would be stupid to give you barbell work in a machine only environment and a body building session when kickboxing is your primary goal.