Presidents are politicians. They must keep in contact with the voters to get re-elected, and the accessibility of the current president has been welcome. It helps defuse concerns about his level of education separating him from ordinary citizens, or forgetting what it's like to be black.
Assessing the strange "what if he'd been carrying a weapon of mass destruction" concerns:
1) The simplest pony yield atom bombs have to weigh at least 40 pounds for the nuclear material alone, based on rough guidelines for U-235 critical mass published in various magazines during my career. Jumping the fence and sprinting across the White House lawn, carrying something that heavy is difficult and _will_ give the Secret Service personnel more time. Such a device would be more effective _outside_ the White House during a semi-public event where the President is outdoors, such as an inauguration.
2) Chemical attacks have similar problems. An aerosol or chemical poison would have to basically flood the air of the White House, which has quite good climate control inside. That means getting past the ventilation system, which would be a _very_ good place to put the sensors and stop the air flow if there were such an attack.
3) Bacteriological weapons would, again, have to get from the attacker's entry to the President. Such a biological agent would be more effectively spread by leaking it during a White House tour, not by a run across the White House lawn.
The Secret Service reacted well, with measured restraint. Better staffed guard posts might be useful, but they are _expensive_. If you estimate the presence of 20 more patrolling guards, 24x7, at roughly $100,000/guard/shift covered, that's roughly $6,000,000/year. Which federal budget shall we strip for that funding?