Filtering by clicking on column

I'm trying to set a table filter by clicking on the corresponding value in a table column using action() (as extraAttributes() gets escaped by blade).
Using the following code
Tables\Columns\TextColumn::make('column.name')
    ->searchable()
    ->alignEnd()
    ->description(__('Some Description'), 'above')
    ->action(function (Model $record) {
        $this->tableFilters['filterName'] = $record->value;
    }),

has no effect.
The column (including the description, unfortunately) is clickable, and a request gets sent, but nothing else happens. Am I missing something? Do I have to tell the component to re-render?
Setting a filter in html using wire:click="$set('tableFilters.filterName', [ '{{ $value }}' ])" does work fine, but is not achievable currently without overwriting the column templates and adding custom code.
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