Agree with some of the PPs, where a 3 yr old's opportunities for practising independence is consistently, across the board, being inhibited (or in extreme cases, actively prevented) by a parent/ parents.
But a good keyworker is aware of the child's overall levels and whether this is simply a needed-by-him reassurance and comfort before Mum leaves, or something more concerning, indicating infantilising by a parent to the detriment of their child.
The resounding message of early years child development/ EYFS should be steer well clear of any "one size fits all, individuality be buggered" commandment allowing no flexibility or respect for different pace in hitting milestones.
Taking NellWilson's example, where her DS was clearly far from "babied", and capable of meeting all nursery requirements and obviously encouraged by her to do so...do you still feel that the cuddle on ground level only, versus in a parent's arms on occasion, is so very vital?
" He was fully dressing himself, and helping me get ready in the morning, and served himself breakfast at home and at nursery. He toileted independently and he followed all the nursery rules about clearing up and sitting on the mat at the right time and so on. And when we got to nursery in the morning, he liked to press the buzzer and then scramble up into my arms for a cuddle on the way inside."
OP also states her 3yr old's similarly independent, bar the need for an arm-held carry/cuddle on arrival ("sometimes", not every single time).
And that it's the rigid insistence he walks in that directly causes the keyworker to have to peel a distressed child off her. Which in itself provides huge reinforcement that clinging to Mum and tears = much attention got, even if negative.
Would think 2minutes being carried (is only through the doorway, for crying out loud!), a quick arms cuddle and a happy kid eager for a fun time at nursery (who will soon enough progress to walking in alone with his classmates merrily doing it and when he feels able) makes the whole handover process less stressful for all concerned?