LGT CLIMBING OUT OF RSW HAD NMAC WITH SMA.

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CLRED BY DEP CTL TO 11000'. AS WE PASSED APPROX 7200' DEP CTL SAID; 'TFC 1 O'CLOCK INDICATES 8700; CONTACT XXX ON XXX.XX; GOOD DAY.' AS THIS CLRNC WAS BEING RECEIVED WE WERE CLBING AT 250 KIAS AT 3000-4000 FPM. F/O LOOKED OUT RIGHT SIDE WINDOW AS SMA FLASHED OVER FUSELAGE AT ESTIMATED 200'. F/O IMMEDIATELY CALLED CTLR (ON NEW FREQ NOW). ATC SAW SMA ON VFR CODE BUT WAS NOT TALKING TO HIM. F/O RELATED OUR EXPERIENCE; BUT CTLR TOLD US IT WAS PLT'S RESPONSIBILITY TO AVOID VFR TFC (I KNOW THAT). I CERTAINLY REALIZE WHAT'S LEGAL AND WHAT MY RESPONSIBILITIES ARE. NEVERTHELESS; WE TRIED TO EXPRESS THE PRACTICALITY OF AN EARLIER WARNING; LAST MINUTE ADVISORIES ARE PRACTICALLY USELESS AT 250K (290 TAS) (DOUBLE THAT FOR 2 ACFT HEAD ON) WITH THE LEGAL 3 MI VIS REQUIRED FOR VFR FLT. DUE TO HISTORICAL AND POLITICAL REASONS WE HAVE ACFT FLYING IN MARGINAL (BUT LEGAL) 3 MI VIS IN AIRSPACE WITH MIL ACFT; BUSINESS JETS AND ACRS; MOST AT 250 KIAS. CONSIDERING TRUE AIRSPD; IT IS POSSIBLE TO HAVE 2 ACFT CLOSING AT VERY HIGH SPDS IN 3 MI VIS. AND; SOME OF THESE ACFT ARE FULL OF KIDS AND GRANDMAS. PERHAPS SOMETHING LIKE A MIL CLB CORRIDOR IS THE ANSWER. AGAIN; I ACKNOWLEDGE THAT IT WAS MY RESPONSIBILITY TO SEE AND AVOID VFR ACFT IN THE SITUATION WE ENCOUNTERED. NEVERTHELESS; I SUGGEST THE FOLLOWING: FOR ATC: 1) GIVE TFC CALLS ASAP; JET ADVISORY SVC IS USELESS WHEN GIVEN AT THE LAST MOMENT AS IS OFTEN THE CASE. 2) RECOGNIZE AND TAKE INTO ACCOUNT THE APPROX PERFORMANCE OF THE ACFT IN COMMON USE (THE LGT CLBS FAST AND DESCENDS SLOW; A CONSTANT PROB GETTING CLRNC TO CLB/CONTINUE CLB OR DSND). THE CLB RATE WAS A FACTOR IN OUR INCIDENT. FOR MYSELF: 1) MAX OUTSIDE LIGHTS BELOW FL180 (LNDG LIGHTS; TURNOFF; TAXI; WING ICE LIGHTS; ETC). 2) NO ACARS RPTS SENT; NO COMPANY RADIO CALLS; NO PAX ANNOUNCEMENTS; BELOW FL180. 3) ATC CONDITIONS PERMITTING; CONSIDER CLBING AT VZF (APPROX 220K) AND REDUCED CLB RATE BELOW 10000'. PERHAPS IT WILL ALLOW JUST A LITTLE MORE TIME TO REACT. 4) MAINTAIN A GOOD LOOKOUT. ASK JUMPSEAT TO ASSIST IF WE HAVE SOMEONE. 5) ABSOLUTELY NO NON OPERATIONAL CONVERSATION BELOW FL180. FOR WHOEVER MAKES THE RULES: 1) 3 MI VIS IS NOT ENOUGH; 250K MAY BE TOO FAST!