Why can't I draw with my touch-screen laptop?

With the proper hardware and software you should be able to freely draw in Photoshop. Photoshop does not support Touch Screen finger painting because the lack the hardware required for Photoshop Brush tools. So  Photoshop supports only touch screen touch gestures.  Touch screen do not have left click button nor does your finger.   Photoshop's Brush tools support hardware that have hardware control features like buttons pressure, tilt and other control features like clicks.  Touch screens do not have these hardware features.  Touch devices  like touch pads, touch tablets like Wacom Intuos pro have accessories and hardware features missing in Touch screens.   Even Wacom Disable Wacom tablet's touch support when you bring you Wacom pen close to your Wacom tablets touch surface.  However, Wacom pen support position the display cursor like a mouse and the left click when you then touch the pen to the actual surface.  With touch screen support you can not position the cursor then touch the screen like you can with a pen.  The cursor is position when you touch the display surface it can not be precisely position then clicked.  Touch screen support also does not support pressure.  A Touch Screen stylus is a single finger substitute has no buttons nor pressure support.  Some Display Devices like Microsoft Surface, Wacom mobile studio, and Cintiq displays support Pen devices.   Pen devices are not the same as a stylus. They have buttons and support pressure.

Paint application brushes support finger painting but brush strokes can not be controlled as precisely as with a pen device. A paint application may be all that you need for your type of painting.  You can save your painting you paint in a paint applications and then work with them in Photoshop.

Use Photoshop Family Customer Community  Adobe's feedback site an request a Finger Paintings feature be added to Photoshop.  Other would also like to se such a feature.  If demand is high perhaps Adobe may add such a feature. Adobe may also think it not a worthwhile addition to add.