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Is it normal to be "too busy" to give a kiss or hug before doing stuff your mind is set on?

Background Info:

I use to want to not touch and love up on my girlfriend due to never doing such before (uncomfortable) and wanting to take things slow, and now the tables have flipped. Been with her for 2-3 years now, love her dearly, and she claims to love me the same, yet it feels like she's always too busy doing stuff to take a moment to feel and appreciate our love.

Whenever I try to catch her leaving or coming in just for a quick kiss or embrace, she either dismisses such by claiming to be "too busy" or aggressively obliges out of frustration. I feel like I'm not asking for much, just 1-5 seconds to take a moment and appreciate what we have is all I want, but maybe I am?

I've discussed such with her before, but we're seemingly reverting back to the same ol' sharades. Usually I'll try and wait for her to finish whatever, but even then she's sometimes like a sack of potatoes and doesn't wanna cuddle much or anything. If she ever does, it's when she's in a particular mood for such.

I've stressed to her how important intimacy is for me, but it seemingly doesn't phase her or she simply keeps forgetting (intentionally or not) and going back to what's normal and easy for her. It makes me feel unappreciated and simply a placebo that any other guy could fill in for her, though she claims otherwise and states she's madly in love with me.

What are your guys and gals opinion? Is this a normal process of long-term relationships? How can this be remedied where I'm not bothering her but she'd be able to and comfortable to show me some loving in the way I want it? Am I asking too much from her? Would more romantic gestures work? I try taking over for whatever it is she's doing sometimes (dishes, cooking, etc) which works sometimes, but generally she's usually always in a groggy mood when she's leaving or coming back home anyways.