This is only true when comparing a 4-stroke engine with a rather simple 2-stroke one. While cooling does not necessarily differ (air-cooled 4-stroke engines exist as well as water-cooled 2-stroke engines), lubrification of simple and cheap 2-stroke engines is often (not always) achieved via mixing some oil into the fuel.
There are highly sophisticated 2-stroke diesel engines as well (eg. rather large engines driving big ships). As well as petrol engines with lubrication via a dedicated system rather than the lubrication via the fuel.
The people factor: mixing too little oil in the fuel causes bad lubrication.
Mixing too much oil causes excessive carbon deposits, carbonizing the piston rings, carbon soot causes scratches in the cylinder linings and piston walls and the spark plug oils up, failing to spark. It also lowers fuel efficiency, as the oil-contaminated fuel burns quicker, needing different spark timing.
The presence of valves provides for optimum fuel consumption and energy availability. Two stroke engines are designed for a happy medium power requirement. Lower or higher power requirements moves engine away from optimum power design point, causing 2 stroke engine to labour under stress. This labouring under heavy power load causes premature failure of the crankshaft journal bearings due to too low turning speed.
A two stroke engine is designed as a cheap and lighter engine solution for mobility and economy.
Quite simply, 2-stroke engine have a power stroke for each revolution, whereas a 4-stroke engine has a power stroke every other revolution. This results in more power for a given displacement but higher average loads on their parts.
Most of the "wear and tear" in these engines tends to be on the cylinder at the top and bottom of the stroke, where the piston comes to rest momentairly, allowing the oil film to break down. The lowest such wear evidently occurred in the "sleeve valve" engine, where the inner cylinder liner is rotating at these times. Descriptions can be found at https://en.wikipedia.org/wiki/Sleeve_valve and https://en.wikipedia.org/wiki/Knight_engine.
As an aside, 2-stroke engines at first glance seem to have the capability of twice the power output as the same displacement 4-stroke engine, due to twice the power strokes, plus the potential for higher speeds due to the lack of poppet valves. This advantage is heavily compromised with A) the loss of effective displacement when the exhaust ports are uncovered, and B) relatively poor "scavenging", or exchange of burnt fuel-air with a fresh charge (also reducing fuel efficiency).
These drawbacks can be largely overcome with the "opposed piston" type of 2-stroke engine (https://en.wikipedia.org/wiki/Opposed-piston_engine), with two pistons entering a cylinder (one from each end, and thus no cylinder head), inlet ports at one end of the cylinder and exhaust ports at the other (see https://en.wikipedia.org/wiki/Opposed-piston_engine for more information). The principle drawback of these engines are that they are not naturally scavenged, usually requiring a turbocharger or supercharger for operation. On the other hand, they can have an awesome power/weight ratio, and have found use in large diesel engines, particularly in ships.
In 4-S or 2-S engines, wear and tear are depend on engines lubricating system or cooling system. 4-S engines have better lubricating system as compare to 2-S engines. So instead of more frictional parts, 4-S engines have less wear and tear phenomenon. If you compare two different 4-S engines then you can find that engine which has better cooling arrangement has less wear and tear problem.