assuming that spiders are actually a serious risk where you live, and if it's a phobia in any way like my own irrational fear of heights, then yes it's a good idea to overcome.
the sudden panic reaction when you perceive something that looks like a spider[0], really isn't going to keep you safe when it counts, while acting calm, rational and with common sense will.
heights can be dangerous but my fear of heights is not doing much of protecting me. the heights I may encounter but prefer to avoid aren't actually dangerous (see-through/grated floors are the worst :) ). the situations that are dangerous, I'd rather have my full faculties if I were to find myself there.
[0] i know people who react very strongly to just an image of a spider. living in NL where there's zero dangerous wildlife (just 1 or 2 endangered species of tiny poisonous snake, a lost/dead wolf every few years and 17M humans), that's quite an irrational fear but I won't mess with that because the panic reaction is very real and involuntarily. For fun, however, we tried an experiment where I very slowly drew a cartoon spider, to see at what amount of legs the reaction would kick in :) turned out drawing tiny hairs on the legs did way more for the response than whether I drew 5,6,7, 8 or 9 legs (at which point the other party didn't think it was fun anymore, so I had to end the experiment). and just in case you wondered yes I play with my own phobia in a similar way, whenever I find myself on a perfectly safe balcony that triggers my acrophobia, I like to see how many minutes I can enjoy the view before the GTFO feeling becomes overwhelming (on balconies it's not quite immediate, but still very strong when it kicks in, making it an interesting process to observe).