Could new satellites be designed to intercept other older functioning artificial satellites or space junk already in orbit to add weight to the new satellite in order to last longer in orbit?
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3$\begingroup$ Adding mass would not slow down orbit decay. You have to improve drag to mass ratio. But only satellites in LEO decay fast. $\endgroup$– UweCommented Dec 18, 2018 at 21:28
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$\begingroup$ @Uwe or small light weight satellites? $\endgroup$– MuzeCommented Dec 18, 2018 at 21:30
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$\begingroup$ @Uwe so yes if the adjoining satellite is in line to the larger satellite not to create more drag? $\endgroup$– MuzeCommented Dec 18, 2018 at 21:32
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1$\begingroup$ @Uwe "Adding mass would not slow down orbit decay." isn't really a good way to say it. If you double the mass of a satellite and increase it's drag by 10% of course it will last roughly 40% longer. I think you mean it wouldn't necessarily, in all cases slow down orbit decay, but it certainly could if done in a reasonable way. Stick the mass on the front or back and it won't increase cross-section or drag very much. $\endgroup$– uhohCommented Dec 19, 2018 at 12:37
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5$\begingroup$ It could help a lot if the "mass" that you add includes a reaction motor, some fuel, and a guidance system. $\endgroup$– Solomon SlowCommented Dec 19, 2018 at 15:08
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There have been projects with this intention, such as OLEV, but actually, this would only allow increasing the life of a satellite from a propellant and orbit maintenance point of view.
Theoretically it is possible, but one would expect other systems in the satellite to fail, particularly the battery would loose maximum charge and panels would loose efficiency over time. You could send an appendix satellite with a new battery to the old spacecraft, but at some point, you are very likely to have enough failures in non-standard devices such as the payload that would are better of launching a new satellite.
Also, there are several projects and discussions about space thugs, which would be able to capture and get rid of space debris. An alledgedly first case would be the RemoveDEBRIS satellite. But in this case, the end goal is to de-orbit a defunct satellite or random debris, instead of amking it last longer in orbit.
Hence, the current practice answers your question with "no, it wouldn't be better", as far a "better" could be understood as whatever governments and the free market have decided to do so far.
Note as well that due to technology improvement, it is unlikely that repairing spacecrafts in orbit will ever be a thing. For instance, while geostationary satellites are designed to last for 15 years, their throughput has been increasing very fast in the few last years, to the point where "The first two ViaSat-3 satellites are expected to deliver more than twice the total network capacity of the approximately 400 commercial communications satellites in space today – combined.". Hence why performing costly repairs on old, low-capacity satellites that are loosing reliability instead of launching new, modern ones?
