Because Dumbledore, for all his faults, was a brilliant commander.
The only thing that was keeping Voldemort out of Privet Drive was Lily’s sacrificial protection, which would cease to exist on and after Harry’s 17th birthday. The only hope for the Order, therefore, was to move Harry before 31st July. In doing so, Lily's protection broke the moment he stepped out of Privet Drive’s vicinity after Dursleys had left their home.
Once the Trace was broken, Moody said Thicknesse would be informed about it, and hence the Death Eaters would know. The Death Eaters, however, had the orders to capture Harry Potter, and not kill him - something Dumbledore knew since the 4th year.
In keeping Harry insights but out of reach, the Death Eaters will be focussed on getting to Harry, rather than killing others in the Order.
Also, this plan served the extremely advantageous purpose of wasting the Death Eater’s time and delaying Voldemort’s arrival.
I am supposing that if the Trace broke, and Harry wasn’t in sight - the Death Eaters wouldn’t have hesitated to target and torture others in the Order.
Also, we wouldn’t have gotten this gem, ha!