Laravel morphs question and error

I'm creating a project where an user can have different profile information

That is the user migration:

        Schema::create('users', function (Blueprint $table) {
            $table->bigIncrements('id');
            $table->string('name');
            $table->string('email')->unique();
            $table->timestamp('email_verified_at')->nullable();
            $table->string('password');

            $table->string('profile_type')->nullable();
            $table->unsignedBigInteger('profile_id')->nullable();

            $table->rememberToken();
            $table->timestamps();
        });

And the advertiser profile (removed the fields for example purposes):

        Schema::create('advertiser_profiles', function (Blueprint $table) {
            $table->bigIncrements('id');
            $table->string('description');
            $table->timestamps();
        });

In the User model:

    protected $with = ['profile'];

    public function profile()
    {
        return $this->morphTo();
    }

In the AdvertiserProfile model:

    public function user()
    {
        return $this->morphOne(User::class, 'profile');
    }

The question: I need to be able to create the user without a profile so the fields profile_type and profile_id should be nullable. I tried to use $table->morphs('profile') but it creates the fields as not null, when trying to use ->nullable() in the $table->morphs it doesn't work. In the docs doesn't mention how to make $table->morphs nullable.

The error: You might noticed that I used protected $with = ['profile']; in the User model so whenever I retrieve an user I will have the profile attached without the need to call it later. The error happens on the opposite side, if I put protected $with = ['user']; in the AdvertiserProfile with the morphOne I get an error saying:

PHP Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 20480 bytes)

How can I solve this?