I believe we should program the way you do nowadays. This is what people praised in the past so much as code reuse. This is what research people call standing on the shoulder of giants. We should reuse other's wisdom (well, you need to filter what wisdom is and what not first, of course, which is not that straightforward itself). Most profession work on pre-manufactured components for the sake of... well, many things (its a story of its own)!
Do it smartly, know what that component is, if that is good for the purpose, if that is the best for the purpose, its trade-offs, but that should be the primary way. With fallback to reinventing the wheel.
We still will have to provide custom built solutions from scratch from time to time (in fact in a lot of cases, the CS is still not mature enough for proper higher level operations) but better to rely on tested and ready pieces.
Recruiters seems to have no clue how to select people for the particular position therefore they go back to the ancient times of CS like this dumb whiteboard thing. I also felt like they seems to expect that custom made employees exists out there and they only need to wait for the perfect candidate, not really expecting someone to learn while the continuous learning is the industry norm, the inherent requirement. I've seen positions remained unfilled for more than 6 months sending away partially fitting experienced candidates.
I failed at technical interview where you must react instantly and accurately without any help normally available in everyday life (Google). After looong time of programming and learning various approaches I find myself question myself continuously even in fundamental matters. Or is it something by age? Nevertheless while being young, self confident and energetic and the Google style of programming was far from invented my fingers were spitting huge amount of brilliant code that did not work until I fixed all the stupid mistakes I made, which took frustrating amount of time. Coding gives a good amount of humility by showing you that you are to blame in every last cases. Every time! Making mistake, misunderstanding something, not knowing necessary elements, misjudging aspects, not checking the reliability of some component you rely upon, it always comes back to you as the computer will do exactly what you tell it to do, it will always be you. Frustrating. I learned to doubt myself and verify seemingly evident matters which does not play well in whiteboard interviews as you might imagine (in fact once I had mental whiteboard interview, speaking about solutions, how common is oral programming in practice?). This is an unnatural and sinfully inaccurate way of judging how one will work in a position. Due to the constantly changing (improving?) profession and the huge amount of beautiful aspects it entails keeping every bit of detail in head that you can spit out in a second notice is far from being a smart expectation. It happened more than once that the right answer occurred me after walking away from the interview as the knowledge bubbled up of the sea of experiences. Once I told someone that sorry, I never met that technique before just to realize later it was an essential component in a task several years back, I used that quite a lot for that one task.
I did not change position too much (3-8 years spent in one place) but I never been hired based on whiteboard test but by trial tasks or probation period, fulfilling the need of the position (leaving due to dissatisfaction every time). In fact I just met whiteboarding recently and I find it hugely inadequate to judge competency.