I mean, they won as Cleveland, and almost won as Tilden, not to mention were a considerably stronger presence in the gilded age overall than during the progressive era (the exception is the age of Wilson). What you're describing is not the folly of being a conservative Democrat, but merely describing the position of the Democratic party post civil war and pre Great Depression party, the party that was not the party of Lincoln. As for their extremely embarrassing defeat in 1924, it was caused largely by a split in the party not along ideological lines, but amongst communal and regional.
And Teddy Roosevelt, a progressive Republican, won the presidency in a landslide, and even the 1920 rise of the conservative branch of the GOP had to do with an anti-Wilsonian backlash in the aftermath of his decision to break his promise in 1916, that is to keep the country out of the first world war: context matters.
(1) IMO 1876 really should have been a winning year for the Democrats, even without the disputed southern states, and Tilden's conservatism was one reason it wasn't.
"There is no question that during the depression of the 1870s taxpayers across the nation felt overburdened, but this program of reducing government expenditures rather than increasing them to deal with economic hardship had a cost. That cost is illustrated by two revealing letters. Immediately after Tilden’s nomination, a furious Kentuckian sent a letter to a Philadelphia newspaper vowing to oppose Tilden and instead marshal support for the separate Greenback candidate who wanted to print more paper money to promote economic recovery. “Our motto,” he wrote, “will be ‘relief’ and not Tilden reform.” Then, on October 25 Horatio Seymour, who had been the Democratic presidential candidate in 1868, wrote the following to Tilden:
"I have reason to know that your opponents in and out of the party count upon the large towns to defeat you. They rely upon deserters among Democrats, hard times & the role of money. The word ‘reform’ is not popular with working men. To them it means less money spent and less work. Most of these men are Catholics. You will see that the Republicans have dropped the school question. I think it important that some quiet judicious person should visit the large towns and see the leading Irishmen and call their minds back to the hostility of Hayes and the Republicans to their nationality & religion. There is danger of a loss of votes among this class.”
"No evidence exists of any substantial swing of Irish Catholics, Democrats’ most loyal constituency, to Hayes in 1876, and even abstention seems unlikely given the growth in the Democratic vote. Unemployed Protestants, however, are another matter. They too wanted an increase, not a decrease, in public expenditures. Tilden, in short, may have bet on the wrong horse. During hard times promises of relief may have trumped reform among all but the silk-stocking Liberal Republicans. With Democrats offering no program for immediate economic recovery and Republicans stirring up still-visceral sectional and religious hatreds, the Republican comeback in 1876 becomes more understandable.'
Visit President Rutherford B. Hayes' wooded estate named Spiegel Grove, home of America's first presidential library. Tour the president's 31-room Victorian mansion, see his tomb, visit the newly renovated museum, explore the library and walk the mile of paved trails.
www.rbhayes.org
(2) As for Cleveland, I'll quote Lipset again:
""It should be remembered that it was a conservative Democrat, Grover Cleveland, who, in 1886, sent the first message to Congress on labor. In it he urged that a commission on labor disputes be set up which could investigate and even arbitrate if so requested by the parties involved or by the state government. In 1888 in his last message to Congress after being defeated for re-election, Cleveland denounced 'the communism of combined wealth and capital, the outgrowth of overwhelming cupidity and selfishness...not less dangerous than the communism of oppressed poverty and toil...'...It is important to note that Cleveland was much more conservative in his second term of office when he no longer had to anticipate facing the voters than in his first one, and that he was repudiated by the Democratic party at its next convention in 1896. In fact, Cleveland was the only President elected in his own right to be repudiated by a convention of his own party while still holding office.."
https://archive.org/details/politicalmansoci00inlips/page/308/mode/2up Bryan lost in 1896 but at least made a respectable race. Can you imagine how a Cleveland Democrat would have done?
(3) TR was pretty much an accidental president. The Republicans would almost certainly not have nominated him for president in 1904 if he had not already become president through McKinley's assassination (Fairbanks seems a more likely candidate had McKinley lived). Once he became president and was enormously popular, they couldn't give up on him, but it is noteworthy that the Democrats in Congress actually supported "Square Deal" measures more solidly than Republicans, who (with some success and the acquiescence of TR) tried to water them down. TR didn't really become radical until after he had left the presidency--and in his role as radical he after all failed to win the nomination in 1912.
(4) Maybe the Democrats were doomed to lose in 1904 anyway, but the fact remains that Parker lost far worse than Bryan ever did. Among other things, he showed that a conservative Democrat couldn't even get the financial support of big business. "The Republicans may appeal with success to the conservatism of the country , ” admitted the anti - Bryan Louisville Courier - Journal after Parker's defeat; "not so the Democrats."
https://www.google.com/search?q=louisville+"not+so+the+democrats"&source=lnms&tbm=bks&sa=X&ved=2ahUKEwjuoczt99DsAhXFna0KHQYEAUgQ_AUoAXoECAUQCQ&biw=1722&bih=902
Indeed, could Hearst have done worse than Parker? After all, Hearst was almost elected Governor of New York in 1906!
(5) 1924 may have been a losing year for the Democrats in any event but if they had nominated someone progressive enough to persuade La Follette not to run, they surely would have done better than 28.8 percent...
Being a progressive was certainly no guarantee of victory for a Democrat in the twentieth century but the two times when the conservative Democratic strategy was tried, it turned out far worse.