Do I really need disability insurance if my employer provides it?

My employer offers short-term and long-term disability insurance. But I keep getting mail from independent agents saying employer coverage "isn't enough."

My employer coverage:

• Short-term: 60% of salary for up to 6 months
• Long-term: 60% of salary until age 65
• No cost to me (employer pays)

The agent said I should get my own policy because:

1. Employer coverage is taxable (reducing effective benefit)
2. Only covers base salary (not bonuses)
3. Goes away if I leave the company
4. "Definition of disability" might be more restrictive

Is this a real concern or just sales tactics? I'm 35, software developer, make $130k base + ~$20k bonus. Family of 4.

Seems like an extra $150/month for something that probably won't happen. But if I became disabled and couldn't code anymore, maybe that 60% wouldn't cut it?