I guess it is possible. However you may not need to inherit components classes to reuse their views. Here's what I did:

Created a CategoryDropdown:

class CategoryDropdown extends Component
{
    /**
     * Get the view / contents that represent the component.
     *
     * @return \Illuminate\Contracts\View\View|\Closure|string
     */
    public function render()
    {
        return view('components.dropdown', [
            'name' => 'category',
            'items' => Category::query()->whereHas('posts')->get(),
            'itemType' => 'category-dropdown-item'
        ]);
    }
}

As you can see, it uses a generic dropdown view, which is the following:

@props(['name', 'items', 'itemType'])

<select name="{{$name}}" id="{{$name}}" class="dropdown">
    {{ $slot }}
    @foreach($items as $item)
        <x-dynamic-component :component="$itemType" :data="$item"/>
    @endforeach
</select>

The trick is the dynamic component, which will be replaced by a CategoryDropdownItem component:

class CategoryDropdownItem extends Component
{
    /**
     * @var string
     */
    public $value;
    /**
     * @var string
     */
    public $text;
    /**
     * @var bool
     */
    public $selected;

    /**
     * Create a new component instance.
     *
     * @param Category $data
     * @return void
     */
    public function __construct( $data = null )
    {
        $this->value = $data ? $data->slug : '';
        $this->text = $data ? $data->name : 'Categories';
        $this->selected = $data ? request('category') === $data->slug : ! request()->has('category');
    }

    /**
     * Get the view / contents that represent the component.
     *
     * @return \Illuminate\Contracts\View\View|\Closure|string
     */
    public function render()
    {
        return view('components.dropdown-item');
    }
}

This one only maps the needed fields of a Category model to be used in the generic dropdown-item view:

<option value="{{$value}}" {{$selected ? 'selected=true' : ''}}>{{$text}}</option>

Note that the category-dropdown.blade.php and category-dropdown-item.blade.php views do not exist! So when I call the components in my posts.index view, that's the component classes that are executed, and then renders the generic dropwn.blade.php and dropdown-item.blade.php views:

<div class="col-4 col-12-mobile">
                                    <x-category-dropdown>
                                        <x-category-dropdown-item/>
                                    </x-category-dropdown>
                                </div>
                                <div class="col-4 col-12-mobile">
                                    <x-author-dropdown>
                                        <x-author-dropdown-item/>
                                    </x-author-dropdown>
                                </div>

Then I did the same for AuthorDropdown and AuthorDropdownItem, still calling the generic dropdown and dropdown-item views.

Extract a Category Dropdown Blade Component

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