If you have concerns that are high enough to place the child on the SEND register, then I think some more conversations with parents need to happen to outline the positives of this. It would also be worth sharing that if they move to another school, you have a duty to inform that school of any assessment data and support/intervention that was in place for the child while on roll with you even if they are not a child with SEND. You also need to share any concerns that you have for children so they these can be monitored as they begin a new placement. Therefore, the new school are likely to make the same decision that you are coming to and see that placing them on the SEND register would be beneficial.
It is also important to explain to parents that being on the SEND register can also support with transition (especially to secondary) and open up more avenues of support for children than those who are not on this. It is also flexible, meaning that once a child is placed on the SEND register, they do not need to be there forever.
Ultimately, I think you may need to spend some more time talking to parents about the positives and how being on the SEND register can ensure that the child is receiving the correct support, wherever they attend school.
I hope this helps.