Oh OP I totally get this and I’m really struggling with it now.
My sister had her kids young (18 and 21) and my mum and dad literally helped raise them.
I was always so close to my parents but was completely pushed out when my niece and nephew were born.
My parents helped my sister with money and she had thousands extra money then I ever did.
They helped her buy a house, paid for her driving lessons, bought her an expensive first car, paid for her wedding, took her and the kids on holiday etc…
I had to work 50/60 hours a week rarely seeing family, no one seemed bothered about what I was up to until my parents were dying of cancer.
Suddenly I was supposed to take time off - despite being single and having no one else to pay the bills and be there all the time. After my dad died my sister dumped her kids so much on my mum I very rarely saw her alone.
My partner lived in an area popular for tourists and my mum loved coming to stay, if it meant she couldn’t look after the grandchildren she spent her whole stay on her phone apologising to my sister.
When my mum was dying my sister was still dropping her kids off with her and wanted me to care for my mum the same amount as her (when she wasn’t working but getting paid) and her kids. I still had to work and it wasn’t possible.
In the nine months between my mum being diagnosed with cancer and then dying I saw her 3 times without my niece and nephew. I went to see my mum one day and she was too weak to get up whilst my nephew was standing on a stool trying to cook a tin of beans with the unopened tin in a frying pan with the gas ring on full.
One thing that I can never forget is my mum
saying to me “I hope you can forgive yourself for not spending more time with me” before she died.
I have never blamed myself for being unable to be at my pmums side 24/7 when I had to work and I’d been pushed out for years.
I got a lot less inheritance because it went to my sister for her kids, my sister still wanted some of what I was left and wanted me to step into my mums shoes with childcare.
I’m still very angry with my parents and hurt despite them being dead, I am NC with my sister and haven’t been since my mum died.
I completely understand the feeling of not mattering when you are childfree compared to siblings that have kids. The boiler example you used was similar to so many similar situations I was in.
I doubt your mum will see your point but don’t feel guilty if you are ever in the situation I was in. If you aren’t important to your parents now then they shouldn’t expect more from you later.