Is it a good idea to switch to hub gear?
No, it is not a good idea.

You'd be spending more than the bike is worth even for a basic internal gear hub (even assuming you got the wheel rebuilt for free using the existing rim and spokes, if possible), let alone buying a rear wheel with an IGH built in. You do need a chain tensioning pulley or horizontal dropouts, which while can be built more robustly than most derailleurs, still is more complicated than most people who want an IGH would deal with and eliminates one of the key advantages. 

If you want better gearing, your best bet is probably to use a different freewheel (TZ71 is a 7 speed shimano freewheel - note that this is not the same as a cassette). If you want a lower gear, you may want to find an old 7 speed Shimano Megarange freewheel (or more likely, you'l probably have to go Sunrace these days). Any higher probably doesn't make much sense (Sunrace makes a 13t I think in 7 speed, but its not buying you much, with that style of bike - just spin faster). 

Removing the wheel with an IGH on that bike would be about as complex as without it due to the pulley, so you're not significantly changing the complexity. Cleaning is about as difficult as well, with a chain cleaner like the Park Tool CG-2, and you still have to oil occasionally either way. 

If you want an easier way to remove the rear wheel, consider getting a quick release wheel if you do not have one already (if you have a solid axle, you could try adding axle release).

But really, with a bike of that quality, you're best off just keeping it running and if you want to do any upgrades, just buy a better bike to begin with and then start upgrading it. If you want to run an IGH, look for something designed for it (likely, it will have horizontal dropouts - think something like Surly CrossCheck).