Do we need a table plan?

That sounds lovely and I think poems instead of name cards is really personalised and informal. I think it would be really different.
I hope you have a wonderful wedding. Me and my fiancé are getting married in Gretna Hall on Halloween next year! X

We went to a wedding recently with no seating plan and it was a bit confusing to be honest, as guests weren't sure where they should sit to leave room in the right place for the bride and groom and their parents or who they would want to sit next to so it kind of had the opposite effect to the relaxed vibe at first. I'd suggest reserving one of the round tables to be a top table for the bridal party as it actually gives people more comfort that they aren't sitting in the "wrong" place - even if you do move about later.

I think it’s best to do a seating plan. Realistically, there will need to be a certain number of people on each table, and you don’t want to end up with 10 people squeezed on to one table and six on another feeling like other people don’t want to sit with them. Do the seating plan, but encourage everyone to get up and chat between courses, if that’s what you want.

Having a table plan will enable your guests to quickly find and take their seats. All they'll need to do is locate their table and name tag according to https://www.topwritersreview.com/reviews/theunitutor/ your seating chart. If you don't have a table plan, every one of your guests will need to scope the room to try and find spare seats that aren't next to strangers.