When you have both main beams on they are drawing about 10Amps through the wiring, connectors and switches. If all this is in perfect condition and up to the job there shouldn't be a problem, but it does appear that the whole system is marginal at best and may give problems with age and usage. Using relays and better quality wiring takes the load off the switches, existing wiring and connectors so as has been pointed out there is less likely hood of a voltage drop at the bulbs, which are very critical, so you get maximum light output. If the whole job is done well there is also far less chance of a total headlight failure due to connectors and/or wiring burning out and switch contacts failing due to arcing debris build up.
