I get difficult babies. Mine didn't have reflux, but was a horrendous sleeper (albiet not as a newborn), had colic, cluster fed, refused bottles and wouldn't be put down without crying.
I still didn't miss a meal. If I was hungry, I made a sandwich. If thirsty, I made a drink. I didn't leave them to cry - thank goodness for slings, multitasking and being able to do things with one arm.
My point is that the 'its impossible to even make a cup of tea' with some babies is patently false because otherwise people wouldn't manage twins, or having a second child. It may feel like there isn't time for those things, but if there truly wasnt, they'd be hundreds of thousands of starving toddlers.
Having a baby that is in discomfort and screaming all the time is hell, but it doesn't prevent anyone from putting some toast in one handed, or with slings or making a drink.
I get that it feels like it. My colicky baby was, it turns out very seriously ill, which is probably why her sleep etc continued to be so bad, and why she was so clingy. She's very susceptible to getting bugs frequently and horrendously now. On days when I've got a 4yo (who still doesn't sleep through and is still in my bed), ill, lying on me, I feel trapped. I don't drink or eat enough because it feels like I can't move as it would disturb her. Where psychic, my husband brings me food and drinks. But if he's not around, I put her in a wrap on me, and get done what I need. I feel trapped but I'm not. It's just that my needs don't feel as important.
I think it's same with babies a lot of the time. It feels like you are trapped and can't pee or need to eat, but could using a sling, but it often doesn't feel like enough of a priority to do so. All of your attention is lazer focussed on them.
It's still a choice though.