Gosh, what a saddening OP - it's such a shame that the culture of some schools leads to teachers feeling so uncomfortable about receiving gifts :(.
I'm a private tutor rather than a teacher, but on the occasions when I have received presents from students and their parents (either for Christmas or as a thank-you when they leave), I've been really touched by the gesture and delighted by the presents themselves. I still have all of the cards, use all of the tins that biscuits came in, remember opening and enjoying the chocolates, and have the gifts themselves. Two of my students bought me a little pink guitar brooch (that looks just like my favourite guitar) which has pride of place in my jewellery box nearly 5 years later, and I regularly use a really sweet David & Goliath mug that one of my more recent students bought me because I once told her how funny I thought her D&G hoodie was.
I hope my teachers felt the same way. My parents bought my Y6 primary teacher a very expensive guitar tuner as a present at the end of the year because he had done his absolute best to make my final year at the school tolerable despite the 6 years of bullying I'd endured there. Considering that he was the only teacher who really believed that it was a problem, gave up a lot of his free time and incurred a lot of grief from the other child's parents in an attempt to solve it, that gift was simply an expression of the very deep gratitude we felt towards him.
I think that the gifts (irrespective of monetary value) are important due to the thought processes involved. Gifts convey appreciation and respect for teachers, who devote a lot more time for their money than they would have to in most other graduate professions. They also serve as an acknowledgement that teachers are not just service providers - they are custodians of the most precious resource our society has, and they are some of the most powerful and lasting role models children will ever have outside of their families. More importantly, choosing and giving gifts to teachers should be recognised as a vital learning experience for the child - it helps them to grow up with the understanding that they should really value their teachers, and it's their first real experience of "giving back" to people outside of the family who have helped them in important ways. When parents take their DC to choose/make the gifts, they teach them that teachers are to be valued rather than taken for granted, and help the child to see the teacher as a whole person with preferences and feelings rather than just as an authority figure. I also remember the warm glow I used to get from choosing or making something I felt the teacher would really like, and seeing him/her opening it - IMO, any tradition that encourages that kind of thoughtfulness and generosity of spirit in young children can should be preserved even if modification (e.g. spending limits) is needed to suit the demographic or culture of the school.