I'll start a bit from afar.
If I remember psychology of Witchers correctly they are a set of ideologically and socially motivated specialists who strive to produce effective result. If this model is correct then cultural reason for Master to have Apprentice would be one of these two:
Help. In real-world trades of martial arts and survival trades Master + Apprentice > Master. In martial aspect - two pair of arms with swords are more dangerous than one. In survival aspect - it is stupid to go to woods alone as you can have someone to keep a guard at night or help you when some incident or decease reduces your mobility.
Reproduction. As apprenticeship is the only way for Witchers to propagate their culture and trade, Master must take care of producing a proper Witcher from Apprentices. To produce a proper Witcher who will survive in their chaotic lifestyle, Apprentice must be ready to overcome chaotic and everyday challenges of his trade, thus he mustn't be clutz. Thus on his own skin, Apprentice must gain familiarity with those situations and become complex enough to become a reliable help to Witcher's cause rather than useless asset.
Now, to the point: how that model can be useful for you case:
"1" could be interpreted as situations when Master + Apprentice work together to break through problems that would be impossible for Master alone to handle. That must be highlighted - Apprentice made difference as minor as it was.
"2" could be interpreted that Master have to make Apprentice work and develop. Thus Master must delegate his Apprentice to do some practical tasks. Ergo Apprentice will be capable to snatch highlight for himself while doing those.
Generally they can play around a question - which problems are solvable only by Master and which could be solved by delegating those to Apprentice. Master can't solve them all - and if he tries and fails - they are in trouble. "So choose carefully... And yeah, clock is ticking!" :P
Also this problem could be approached from another angle:
Although Witchers' trade is very close to natural selection, which should produce Masters who should be quite keen and experienced there are some catches. First of all natural selection is not "what doesn't kill you makes you strong". Rather than that, natural selection is "what doesn't kill you makes you a crippled mess". Master could have long-term problems like missing limbs or concussion.
Another aspect I clashed with while dealing with kids is - all people are different. Apprentice could be more useful than his Master for approaching different social/physical situations because of his (for example):
- size(perhaps he can sneak into the hole his Master can't),
- weight (perhaps can climb to the tree higher before it breaks, perhaps can pass through the flimsy bridge),
- youth(seduction attemts? health checks?),
- naiveness(he can lie to guard better about things that Master lied to him because he really-really believes that those are truth :P).
Also Witchers are not that sociable creatures so Apprentice with good "charisma" (which stems from his character born from the way his brain works) whose personality is good for connection to people could be more useful sometimes than angry, cold, effective and slightly insane Master.