No, there is nothing wrong with using a bread machine, only the way you use it. Bread machines are awesome for getting you out of the kitchen and still having your bread freshly baked. However, for bread newbies, and especially if using sourdough, I would still recommend using an oven to bake, so you can have more flexibility to change or observe the dough's behaviour while you're learning.
"Hard to cut and the middle doesn't stay put when I tear/bite a slice" - this tells me your bread is lacking structure (not enough gluten).
My biggest suspicion is of your starter, because you also mention problems with flavour.
It needs to be mature/stable before you use it - is yours? Immature (eg been in existence less than ~1.5-2 weeks) or unstable (eg overly hungry) starters can sometimes inadvertently destroy gluten, even if they're otherwise rising fine. Too much acid in the starter can destroy gluten too.
If not the starter, I would say that at some point during the fermentation/kneading the gluten started getting destroyed. Maybe it was overkneaded, or overproofed. Overkneading: might have happened on a very long machine cycle in combination with bread flour. Overproofed: the machine may not have completely beat the gluten apart but the subsequent rise did (though not enough to make it a brick).
If this was in a bread maker knead+bake cycle and you weren't watching, you unfortunately don't have the benefit of knowing what happened. It doesn't mean you have to not use the bread maker. Just open the lid and watch it the whole time, except when baking.
Looking forward to seeing more bread from you!
My $0.02: don't trust anyone that talks about bread with regard to cups. The amount of flour in a cup varies wildly depending on how you scoop it, pour it, or pack it in. Re salt, 1 tsp salt is good for about 300g flour - a rule of thumb is 2% of flour weight. Your salt amounts don't seem too far off, unless your 3 cups contained a lot more flour than 300g. Also, you may wish to find a recipe that uses weight measurements.