Does concentration remain constant in an electrochemical cell's half cells?

We have from Nernst equation:

$$\mathrm{E_{cell} = E^\circ - \dfrac{RT}{nF} \ln Q_c}$$

But I was wondering that in a simple cell like Daniel cell if concentration of $$\ce{Zn^{2+}}$$ keeps increasing and that of $$\ce{Cu^{2+}}$$ keeps decreasing, won't the value of $$\mathrm{Q_c}$$ keep increasing? In that case, won't that lead to a decreasing emf? If it does, then what's the use of such a cell that yields decreasing emf?

• Batteries don't last forever. Aren't you just making that claim? – Zhe Oct 5 '18 at 13:36
• Note that because you have a logarithm, the value of $\ln Q_{c}$ stays relatively constant for larger changes in the value of $Q_{c}$, implying that the battery can maintain a reasonable EMF as you use it up. – Zhe Oct 5 '18 at 13:36

But I was wondering that in a simple cell like Daniel cell if concentration of $$\ce{Zn^{2+}}$$ keeps increasing and that of $$\ce{Cu^{2+}}$$ keeps decreasing, won't the value of $$\mathrm{Q_c}$$ keep increasing? In that case, won't that lead to a decreasing emf?
These cell are still useful. Astute engineers know this and design around it using batteries that provide more voltage than needed when charged. If I have a $$\pu{3.3 V}$$ circuit, I can use a $$\pu{3.7 V}$$ Lithium battery (note $$\pu{3.7V}$$ is the charged voltage) to run the device without damaging it and will continue to work until the battery declines to below $$\pu{3.3V}$$ (actual/rated voltage). Similarly car batteries are typically rated for $$\pu{12V}$$ but if you measure it with a galvanometer (voltmeter) you will find the voltage is on the order of $$\pu{13-14V}$$.